Stat 110 رياضيات واحصاء السنة التحضيرية دوري اول 1438/1439.

Transcription

1 Stat 110 دوري اول 1438/ محمد عمران السنة التحضيرية رياضيات واحصاء

2 stat 110 Ch 1 تعار ف ومصطلحات هاااامه Statistics االحصاء Is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from the data اإلحصاء هى العلم الذي هتم بجمع وتلخ ص وتحل ل ومه ثم وضع االستىتاجات Variable المتغ ز Characteristics or attribute assume different values المتغير خصائص تأخذ عده قيم Random variable المتغ ز العشىائ Have values that are determined by chance المتغ ز العشىائ هى مقدار أخذ ق ما مختلفة حسب وت جة التجزبة العشىائ ة Population المجتمع Sample الع ىة Data set مجمىعه الب اوات Data الب اوات Consist of all subject that are being studied المجتمع تكىن مه جم ع العىاصز ق د الدراسة Is a group of subjects selected from population الع ىة ه مجمىعه جزئ ه مه المجتمع وتمثل المجتمع Is collection of data values are the values that variables can assume Each value in the data set is called data value محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

3 stat 110 Ch 1 االحصاء االستداللى هو عمليه التعميم من العينه للمجتمع فى االحصاء االستداللى نقوم باختيار الفروض وتحديد العالقات بين المتغيرات ووضع التبؤات كلمات مصاحبه لالحصاء االستداللى soonالحديث -maybe-next-can-will عن المستقبل االحصاء الوصفى هى جمع وتنظيم وتلخيص وعرض البيانات فى الماضىوالحاضر كلمات مصاحبه is-was-wereaverage-mean -median - لالحصاء الوصفى modeتاريخ من الماضى محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

4 stat 110 Ch 1 Example In each of these statements. Tell whether descriptive or inferential statistics 1 In the year 2020,148million American will be enrolled in an HMO inferential 2 3 Nine out of ten one-the-job fatalities are men Expenditures for the cable industry were 5.66$billion in 1966 descriptive 4 The median household income for people aged is $ Descriptive 5 Drinking decaffeinated coffee can raise cholesterol by 7% Inferential 6 The nation average annual medicine expenditure per person is 1052$ Descriptive 7 Experts say that mortgage rates may soon hit bottom Inferential محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

5 stat 110 Ch 1 العينه العشوائيه all units of population has thesame chance of selecting العينه العنقوديه فيها يكون المجتمع مقسم الى مجوعات رئيسيه نختار من هذه المجموعات بعض المجموعات ثم نستخدم جميع عناصر المجموعه المختاره العينه الطبقيه فيها يقسم المجتمع الى مجموعات غير متقاطعه ومستقله تسمى طبقات غير متداخله طبقا للنوع )ذكر-انثى (او الجنسيه )مصرى -سعودى - هندى...( العينه المنتظمه -فيها يقسم المجتمع مجموعات عددها يساوى افراد العينه المختاره -يتم اختيار حاله من المجموعه االولى عشوائيه فاذا كان تربيها Aمثال نختار الحاله التى تربيها A -بعض الكلمات الداله 10th...seventh تكون فيها كل حاله من حاالت المجتمع لها نفس فرصه االختبار )اختيار عشوائى بدون شرط ) محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

6 stat 110 Ch 1 Example Classify each sample as random, systematic, stratified, or cluster 1-in a large school district, all teachers from two buildings are interviewed to determine whether they believe the students have less homework to do now than in previous year (cluster ). 2-every seventh customer entering a shopping mall is asked to select her or his favorite store (systematic) 3-nursing supervisors are selected using random numbers in order to deter mine annual salaries (random) 4-every 100th hamburger manufactured is checked to determine its fat content (systematic) 5-mail carriers of a large city are divided into four groups according to gender (male or female) and according to whether they walk or ride on their routes.then 10 are selected from each group and interviewed to determine whether they have been bitten by a dog in the last year (stratfied ) محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

7 stat 110 Ch 1 - متغيروصفى)نوعى( مثل اللون )احمر-اخضر-...الخ( فصليه الدم A-AB-O-( )B متغير كمى مثل age العمر length الطول weight الوزن salary الراتب منفصل مثل عدداالطفال فى االسره عدداالقالم اى جمله تجد بها كلمه number of متصل اومستمر مثل والتريب هنا مهم مثال المستوى التعليمى )ابتدائى -متوسط-...( المستوىاالكاديميى A-B-( )C-D-E-F الوزن -الطول-العمر اى متغير يكون بيه كسور وارقام وفواصل عشريه تريبى االسميه والترتيب هنا غير مهم مثال اللون احمر-اخضر - ازرق....الجنسيه مصرى - سعودى... النوع ذكر- انثى فصيله الدم A-B-( )AB-O محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

8 stat 110 Ch 1 Ex Classify each variable as qualitative or quantitative 1 number of bicycle sold in 1 year by a large sporting goods store quantitative 2 colors of baseball caps in a store qualitative 3 time it takes to cut a lawn quantitative 4 capacity in cubic feet of six truck beds quantitative 5 classification of children in a day-car center (infanttoddler-preschool qualitative 6 7 weights of fish caught in lake George marital status of faculty members in a large university quantitative qualitative محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

9 stat 110 Ch 1 Ex Classify each variable as discrete or continuous 1 number of doughnuts sold each day by doughnut heaven discrete 2 water temperatures of six swimming pools in Pittsburgh on a given day continuous 3 lifetime in hours of 12 flashlight batteries continuous 4 number of cheeseburgers sold each day by a hamburger stand on a collage campus discrete 5 number of DVD rented each day by a video store discrete 6 capacity county (in gallons) of six reservoirs in Jefferson continuous محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

10 stat 110 Ch 1 ex bloodtype (A-B-AB-O) gender (male- ( femaleهى بيانات اسميه التريب فيها مهم ex grade of course(ab-c-d-f) rating scale (poorfiar-goodexcellent) ranking of tennis player وهى بيانات وصفيه )نوعيه ) الترتيب فيها مهم ex heightweigt,age وهى بيانات النسبه اى كل البيانات التى تحتوى على اعداد موجبه او صفر ex temperature IQ test وهى بيانات كميه تكون فيها االعداد الموجبه والسالبه محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

11 stat 110 Ch 1 Classify each as nominal level, ordinal level, interval level, or ratio level measurement Ex pages in the city of Cleveland telephone book ranking of tennis players weights of air conditioners Temperatures inside 10 refrigerator salaries of top five CEO in the united states rating of eight local plays (poor, fair, good, )excellent Ordinal ordinal ratio interval Ordinal Ordinal time required for mechanics to do a turn up ages of students in a classroom marital status of patients in physician's office ratio ratio Nominal 10 horsepower of tractor engines ratio محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

12 stat 110 Ch 1 دراسه مشاهده تتم دون تدخل الباحث مثال عدد المرضى الذين تم شفاؤهم من مرض معين كلمات داله عليه see-find... دراسه تجربييه يحدث فيها تدخل للباحث فى الظاهره محل الدراسهثم مالحظه مدى تاثير هذا التدخل على النتائج مثال اعطاء المرضى عقار معين ثم مالحظه تاثير هذا العقار على عدد تم شفاؤهم الكلمات الداله عليه هى placedon-given... The independent variable or explanatory variable المتغ ز المستقل )المؤثز( Is the one that is being manipulated by the researcher EX - Drug -Method of study The dependent variable or outcome variable المتغ ز التابع )المتأثز( وهى واتج عه المتغ ز المؤثز Is the resultant variable Ex Blood pressure Level of sugar in blood محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

13 stat 110 Ch 1 Example For the following studies, define the type of study, the independent and dependent variable 1-subjects were randomly assigned to two group and one group was given an herb and the other group a placebo. After 6 months, the numbers of respiratory tract infections of the groups were compared Type of study.. experiment Independent variables.herb Dependent variables..group of subject 2-a researcher stood at a busy intersection to see if the color of the automobile that a person drives is related to running red lights Type of study.observational Independent variables.researcher Dependent variables 3-a researcher finds that people who are more hostile have higher total cholesterol levels than those who are less hostile Type of study.observational Independent variables.researcher Dependent variables.. 4-subjects are randomly assigned four groups. Each group is placed on one of four special diets- a law-fat diet, a high- fish diet, a combination of low-fat diet and high- fish diet, and a regular diet. after 6 months, the blood pressures of the groups are compared to see if diet has any effect on blood. pressure Type of study..experiment Independent variables..type of diet Dependent variables blood presser محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

14 stat 110 Ch 1 Test bank 1.Classify each variable as qualitative or quantitative Number of bicycles sold in one year by a large sporting goods store Colors of baseball caps in a store Times it takes to cut a lawn Classification of children in a day-care center (infant, toddler, preschool( Weights of fish caught in the red sea marital status of faculty members in a large university 2-Classify each variable as discrete, continuous, ordinal or nominal Number of doughnuts sold each day by a doughnuts store Water temperatures of six swimming pools in Jeddah on a given day Weights of cats in a pet shelter Lifetime (in hours) of 12 flashlight batteries Number of cheeseburgers sold each day by a hamburger stand on a college campus Number of DVDs rented each day by a video store Capacity (in gallons) of six dams in Saudi Arabia Ages of people working in a large factory Number of cups of coffee served at a restaurant The time it takes a student to drive to school Nationality of people who are living in Saudi Arabia Rankings of tennis players Weights of air conditioners Temperatures inside 9 refrigerators Ratings of eight local plays (poor, fair, good, and excellent) محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

15 stat 110 Ch 1 Times required mechanics to do a tune-up Ages of students in a classroom Levels of services Number of bags Classification of automobiles as subcompact, compact, standard, and luxury 3.Classify each sample as random, systematic, stratified, or cluster Nursing supervisors are selected using random numbers in order to determine annual salaries Every seventh customer entering a shopping mall is asked to select her or his favorite store Every 100th hamburger manufactured is checked to determine its fat content Mail carriers of a large city are divided into four groups according to gender (male or female) and according to whether they walk or ride on their routes. Then 10 are selected from each group and interviewed to determine whether they have been bitten by a dog in the last year In a large school district, all teachers from two buildings are interviewed to determine whether they believe the students have less homework to do now than in previous years. محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

16 stat 110 Ch 1 Select the best answer The number of absences per year that a worker has is an example of what type of data a) Nominal B) Ordinal c) Discrete d) Continuous A researcher divided subjects into two groups according to gender and then selected members randomly from each group for his sample. What sampling method was the researcher using? a) Cluster b) Random c) Systematic d) Stratified Data that can be classified according to color are example of what type of data a)nominal b) Discrete c) Ordinal d) Continuous The number of minutes needed for a student to reach KAU from his home is a) ordinal b) Nominal c) Continuous d)discrete Students' registration numbers (Identification numbers) are example of... data a) Ordinal b) Nominal c) Continuous Which of the following correctly describes the relationship between a sample and a population? a) A population and a sample are not related b) A sample is a group of subjects selected from a population to be studied c) A sample is a group of populations that are subject to observation d) Discrete An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car buyers. The list includes 2,500 Ford buyers, 2,500 GM buyers, 2,500 Honda buyers, and 2,500 Toyota buyers. The analyst selects a sample of 400 car buyers, by randomly sampling 100 buyers from each brand. Is this an example of a simple random? b) Yes, because car c) No, buyers of every brand because every were equally possible 400- represented in the buyer sample sample did not have an a) Yes, because each buyer in the sample had an equal chance of being sampled equal chance of being chosen d) A population is a group of samples that may or may not be included in a study d) No, because the population consisted of purchasers of four different brands of car محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

17 stat 110 Ch 1 Researchers obtain stratified samples by dividing the population into a) Subjects b) Groups c) Variables a) Discrete b) Continuous c) nominal d)ordinal Salaries of the staff in King Abdul-Aziz University are a (an) variable. a) Discrete b) Continuous c) nominal Lifetime of an electronic device is a (an) variable a) Discrete b) Continuous c) nominal..a variable that takes whose values in an interval a) Discrete b) Continuous c) nominal d)ordinal d)ordinal d)ordinal A high school counselor uses a computer to generate 50 random numbers and then picks students whose names correspond to the numbers. This is an example of a) Random sampling b) Cluster sampling c) Stratified sampling d)systematic sampling Listing discharged hotel customers, numbering the customers and using random number table to obtain sample is an example of a) random sampling Discrete variables a) The in an experimental study is the one that is being manipulated by the researcher. b)cluster sampling B) A consists of all subjects (human or otherwise) that are being studied. c) Stratified sampling C) assume values that can be counted. D) systematic Sampling D) are the values (measurements or observations) that the variables can assume محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

18 stat 110 Ch 1 Frequency Distribution A)A represents data that occur over a specific period of time A statistic is B)The is the number of data values contained in a specific class C)The are used to separate the classes so that there are no gaps in the frequency distribution. D)the...is the organization of raw in table form,using classes and frequencies a)defined as the sum of the lowest and highest values in the data set, divided by 2 b)the midpoint of the data array Which statement belongs to inferential statistics? c) a characteristic or measure obtained by using the data values from a sample a)the average life in Jeddah 75 years b)a diet high in fruits and vegetables will lower blood pressure The ID Number is variable c) in 2020, the number of high school graduates will be 4 million students d) B and C a)discrete b)qualitative c)quantitative d)ordinal The measurement Scales of ( Flight Classes ) is a)discrete b)ordinal c) continues d)nominal Which of the following statement is a Stratified Sample a)in football club the coach select 11 players by using chance method to play the final game b)in the KAU, all students from four colleges are interviewed to determine whether they believe the students have less home work to do now than in previous years c)researcher divided subjects into two groups according to gender and then selected members from each group d)every tenth customer entering a restaurant is asked to select her or his favorite salad محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

19 stat 110 Ch 1 In this study determined the independent variable. The teacher divides the class randomly into two groups "group A" and "group B." In group A, the teacher uses a new teaching method to teach the math lesson. In group B, the teacher uses a standard teaching method to teach the math lesson. The teacher compares final test scores at the end of the semester to evaluate the success of the new teaching method compared to the standard teaching method. a)gender b) group name c)teaching method d) final test score is a group of subjects selected from a population. A)a sample b) a population c) descriptive statistics nferential statistics The number of films on one-day in television channel, is what type of data? A)random sample B)continuous C) stratified sample D) discrete 4-For the following studies, define the independent and dependent.variables A-Subjects were randomly assigned to two groups and one group was. given an herb and the other group a placebo. After 6 months, the numbers.of respiratory tract infections of the groups were compared Independent variables. Dependent variable.. B-Subjects are randomly assigned to four groups. Each group is placed on one of four special diets a low-fat diet, a high-fish diet, a combination of low-fat diet and high-fish diet, and a regular diet. After 6 months, the blood pressures of the groups are compared to see if diet has.any effect on blood pressure Independent variables Dependent variable محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

20 stat 110 Ch 1 5-Determine whether each statement is true or false. If the.statement is false, explain why A-When the population of college professors is divided into groups according to their rank (instructor, assistant professor, etc.) and then several are selected from each group to make up a sample, the sample is called a cluster sample B- The variable age is an example of a qualitative variable C. The weight of pumpkins is considered to be a continuous variable.use the best answer to complete these statements 1- Two major branches of statistics are.. and.. 2- The group of all subjects under study is called a(an).. 3-A group of subjects selected from the group of all subjects under study is called a(an) محمد عمزان ر اض ات واحصاء للمزحله الجامع ه /

21 مد م ح عمران حماضرات اون الين زياره الموقع لالستفسار حاله في عدم الرد نرجو ترك رساله باالسم والمادة

22 Stat 110 Ch 2 Type of frequency distribution انواع التوز عات التكرار ة 1-cotegorical frequency distribution انت ز غ انتكراري انتص ف ستخدم ف حاله الب انات االسم ة والترت ب ة ستخدم ف حاله الجداول الت تحتوى على ب انات اسم ه فقط )الجنس ة فص لة الدم النوع ) انت ز غ انتكراري انغ ر يب ة ستخدم ف حاله الب انات الكم ة ذات المدى القص ر انت ز غ انتكراري ان ب ة ستخدم مع الب انات الكم ة ذات المدى الكب ر المدى =أكبر ق مه أصغر ق مه Ex 1)Ahmed wants to construct a frequency distribution for major field of college student's.what type of distribution should be used 1-ungrouped 2-grouped 3-categrical 2) 30 students recorded the colors of their eyes choosing from brown, blue, and green and black this data can be approximately summarized in A-categorical frequency distribution B-grouped frequency distribution C-grouped frequency distribution 1 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

23 Stat 110 Ch 2 التوز عات التكرار ة المبوبة ستخدم ف حاله الب انات الكم ة المتصلة ومدى هذه الب انات كب ر فتقسم إلى فئات )فترات( ولكل فئة تكرارها مثل. - أطوال مجموعه من الطالب وأعمارهم يالحظبث بي 1- عدد الفئات فضل إن كون من 5 إلى فضل إن كون طول الفئة width( )class عدد فردى 3- الفئات جب إن تكون متصلة ال وجد فراغ ب ن الفئة والفئة التال ة 4- طول الفئة جب إن كون منتظم )متساوي( Classes lower class limit upper class limit 0.5 من النها ة الصغرى للفئه Lower boundary 12-.5=11.5 تسمي الفئة العدد 12 يسمي النهبية الصغرى للفئة العدد 18 يسمي النهبية العظمي للفئة لك نوجد حدود الفئة السفلى نطرح خانه عشر ه لك نوجد الحد العلوي للفئة نجمع 0.5 على النها ة العظمى للفئة Upper boundary =18.5 Then class boundary يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

24 Stat 110 Ch 2 Class width =upper boundary lower boundary طول الفئة = الحد العلوي الحد السفلى Class width is =7 class boundary ال ك انحص ل ػهى يهح ظ بي classإال width ي Midpoint = = Midpoint= Notes إرا كب ج انفئت ب ب فبصه ػشر أي انفبصهت بؼذ رقى طرح أ ج غ 0.05 يثبل Lower boundary = =11.45 Upper boundary = =15.55 Ex 1-find class boundary, mid-point and class width for each A) Sol Lower boundary =56-0.5=55.5 Upper boundary =74+0.5=74.5 Class boundary = يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

25 Stat 110 Ch 2 B) Sol Lower boundary = =13.55 Upper boundary = =14.75 Class boundary C) Sol 4 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

26 Stat 110 Ch 2 Frequency Relative frequency انتكرار ان سب تكرارالفئه Relative frequency = = مجموع التكرارت Sum of relative frequencies =1 مجموع التكرارات النسب ة =1 Percentage= Sum of percentage frequencies=100% يج ع انتكراراث ان ئ ت =%011 Ex 1-distribution that are used when the proportion of the data is more important than the actual number of the data are know A-frequency distribution B-open ended distribution C-relative frequency distribution 2-the graphs that their distribution as proportions instead of raw data as frequencies are called A-frequency polygons B-o give graphs C-histogram d-relative frequency graph 3-expect for rounding error, relative frequency should add up to A-0 b- 1 c- 50 d يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

27 Stat 110 Ch 2 for the following table Blood type A B O AB Frequency The sample size is a-60 b-25 2-the percentage of blood type O is a-36% b-20% 3-the relative frequency of blood type A a-0.45 b-0.28 c-30 c-30% c-0.16 d-100 d-16% d-0.2 Sol 1-sample size= =25 2- percentage O= The of observation in a class is called a (an ) in a categorical frequency distribution a-interval b- category c-frequency d-midpoint the blood types of eight students are O,O,B,A, A,AB, O and AB.what are these ungrouped data called? a-raw data b-category c-class frequency d-relative frequency 6 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

28 Stat 110 Ch 2 1-what is the lower class limit in the class 13-17? a-13 b-17 c-12.5 d-17.5 a-13 a-13 a-3.1 a the lower boundary in class b-17 c-12.5 lower boundary = class midpoint in class b-15 -midpoint = c the class width for the class b-3 c-6.55 lower boundary = =5.05 Upper boundary = =8.05 Class width = =3 5-the class midpoint for the class limit b-7.2 c-6.55 d-17.5 d-17.5 d-2.9 d-3 6-in frequency distribution, the number of classes should be between a-5and 20 b-10and20 c-10and 25 7-if frequency distribution has class boundaries of , what would be the class width? a-5 b-6.3 c-5.1 d-8 class width = ==5 7 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

29 Stat 110 Ch 2 Graphs Histogram المدرج التكراري ستخذو ن صف انك بث ان تصهت ػببرة ػ أػ ذ رأس ان ح ر األفق x-axis ثم حذ د انفئت class boundary ان ح ر انرأس y-axis ثم انتكرار frequency The frequency polygon ان ضهغ انتكراري ان ح ر األفق x-axis ثم midpoint ان ح ر انراس y-axis ثم ػه frequency صم ب ان قبط The ogive graph (cumulative frequency graph) ان ح ى انتكراري ان تج غ انصبػذ ان ح ر األفق x-axis ثم ػه class boundary ان ح ر انراس y-axis ثم ػه انتكرار ان تج غ انصبػذ cumulative frequency 8 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

30 Stat 110 Ch 2 Ex Construct a histogram, frequency polygon and o give for the data show Class limits Frequency Solution Histogram Class boundary Frequency يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

31 Stat 110 Ch 2 Polygon Midpoint Frequency class class يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

32 Stat 110 Ch 2 O give Class boundary Less than 0.5 Less than 5.5 Less than 10.5 Less than 15.5 Less than 20.5 Cumulative frequency = = = =69 total frequency cumulative frequency خط frequency( )cumulative class boundary 11 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

33 Stat 110 Ch 2 Summary Class limit Class boundary Frequency Relative frequency Cumulative frequency Cumulative relative frequency = = = = = =1 Total 1 12 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

34 Stat 110 Ch 2 Ex 1-histogram is suitable for represent in data a-ordinal b-continuous c-nominal d-qualitative 2-which type of graph represent the data by using vertical bars of various height to indicated frequency? a-histogram b-ogive c-frequency polygon d-cumulative frequency 3-the is the assume of frequencies accumulated to upper boundary of class in the distribution a-frequency polygon b-cumulative frequency c-relative frequency 4-the graph that represents the cumulative frequencies for the class in a frequency distribution is called a(an) a-o give b-time series c-histogram d-bar chart 13 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

35 Stat 110 Ch 2 f f د سمبر In above graph? 1-what type of this graph a-o give b-pie chart c-petro chart d-histogram 2-the class that has height frequency a b c d the class with frequency1000 is a b c d the total frequency of the data shown a-6000 b-8000 c-7500 d يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

36 Stat 110 Ch 2 Class boundary ages Frequency number of student Given the following distribution 1-number of students where age is less than 23.5 is 1)9+4=13 a-4 b-9 c-13 d-5 2-number of students where age is less than33.5 a-15 b-57 c-40 d-25 2) =25 the number of patient in the waiting rooms. Within a hospital at a specific time are given by the following frequency distribution Number of patient Total Frequency ? that can be best represent graphically by a-frequency polygon b-histogram c-time series graph d-bar chart 2-the missing frequency for the following class is a-10 b-7 c-9 d-8 2) 32-( )=9 3-the sample size is a-30 b-15 c-32 d-5 4) 3+0.5=3.5 4-the upper class boundary for the third class is a-3.5 b-11.5 c-10.5 d the percentage of the number waiting rooms that have 3 patient a-12.5% b-13.33% c-36.67% d-34.37% 15 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

37 Stat 110 Ch 2 Grades boundary Cumulative frequency Use the data given to answer 1-the frequency of the third class a-66 b-42 c-16 d-24 2-the class limits for the second class boundary is a b c d the class midpoint of the fourth class a-58 b-62 c d the sample size is a-79 b-cannot determined c- 203 d- 5 5-what is the value of the highest cumulative frequency? a-69 b- 79 c-cannot determined d-1 6-what is the percentage of students who have marks of at least 55? a-77.22% b-46.84% c-30.38% d-88.18% 7-what is the class width? a-12 b-6 c-4 d-5 8-the best graph for representing the data shown in the previous table is called a-time series graph b-frequency polygon c-histogram d- ogive sol 1) 42-18=24 2) =50, =54 class limit ) 4) 79 5) 79 6) ( ) 7) =5 16 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

38 Stat 110 Ch 2 Other types of graph Is 1-apareto chart used to represent a frequency distribution for a categorical variable ستخدم ف المتغ رات الوصف ة خطوات الرسم 1 -نجعل األعمدة متساو ة ف عرضها 2 -نرتب الب انات من التكرار من االكبر الى االصغر 2-a time series graph Represent data that occur over a specific period وهو مثل الب انات الت تحدث ف فتره زمن ه 17 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

39 Stat 110 Ch 2 3-a pie graph وه دائرة تقسم الى قطاعات كل قطاع حسب النسبة المئو ة للتكرار The purpose of the pie graph is to show the relationship of the parts to the whole We use a pie graph with nominal variable or categorical variable Degree = Degree Relative frequency = Percentage 18 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

40 Stat 110 Ch 2 Example 1-on a petro chart the frequencies should be represent on the A)x-axis b)y-axis 2-what is the other name for the o give a)histogram b)frequency polygon c)cumulative frequency graph 3-data collected over period can be organized into a)time series b)pie graph c)histogram 4-what graph should be used to show the relationship between the parts and the whole a)histogram b)pie graph c)o give 5-in a pie graph if a pepperoni pizza were 24/72 of the distribution, how many degree be needed to represent a pepperoni a)120 b)60 c)90 d) in a pie graph if the blood type O was 36% of the distribution, how many degree would be needed to represent type O? a)120 b)129.6 c)1296 d)360 7-in a pie graph if the blood type O represent by 90, then the relative frequency of the blood type O a)0.43 b)0.5 c)0.18 d) an automobile dealer want to construct a pie graph to represent type of cars sold in July.he sold 72 cars, 16 of which were convertibles the convertibles will represent, how many degree in the circle a)100 b)60 c)50 d)80 19 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

41 Stat 110 Ch 2 the following table represent the favorite car make for a group of student Class Toyota Nissan Chevrolet GMc Honda Frequency the sample size is A)60 b)18 c)5 d) =78 2-if a pie graph is used to represent the data, the degree for G M C brand would be a)0.15 b)55.38 c)0.55 d) the percentage of students who like Nissan is a)30% b)25% c)19.23% d)83.33% 4-the cumulative frequency for the third class is a)13 b)48 c)35 d) =48 5-the type of data a)discrete b)continuous c)nominal d)variable 21 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

42 Stat 110 Ch 2 A stem and leaf plot هو رسم ب ان ستخدم جزء من الب انات لتمث ل الورقة leaf )وه خانه اآلحاد( والجزء الباق مثل الساق )stem( Definition A stem an leaf plot is the graph that retains the actual data while they in a graphic form Ex Construct a stem and leaf plot for the data 25, 13,31,20,32,14,43,2,57,23 Solution نرتب الب انات ترت ب تصاعد ا 2,13,14,20,23,25,31,32,43,57 Stem Leaf What the stem and leaf of 45 a)stem 5 leaf 4 b)stem 4 leaf 5 what is the stem and leaf in 127 a)stem 1 leaf 27 b)stem 12 leaf7 c)stem27 leaf1 d)stem 7 leaf 12 the..is a method of organizing data and it is a combination of sorting and graphing a)pie graph b)stem and leaf plot 21 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

43 Stat 110 Ch 2 test bank 1. The following data represent the fire in the week for 4 cities. Choose the correct frequency distribution to organize the data Class Frequency Limit Class Frequency Limit A Class Frequency Limit Class Frequency Limit b c d 2. What are the boundaries of ounces? a) ounces b) ounces c) ounces 3.The class width for the class is a) 5 b)6 c)33 d)28 The following table shows the frequency distribution of temperature (in degree centigrade) of 30 countries : Class Frequency Limit Use the above table to answer questions(4-6) The number of countries with temperature less than 44.5 is a) 8 b) 10 c) 3 d) 23 5.The percentage of values in second class is : a) b)16.67 c) d) The midpoint in the first class is: a) 32 b)32.5 c) 37 d) يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

44 Stat 110 Ch 2 Use the following graph to answer the question (1-3) 1.The graph has peak a) Four b) one c) three d) two 2.Type of graphs is: a) Frequency polygon b) ogive c)cumulative frequency 3. Other name for ogive is: a) Histogram b) Frequency Polygon c) Cumulative frequency graph d) Pareto Chart From the ogive below, answer (4-5) 4. Approximately what is the total number of observations? a) 222 b) 50 c) 8 d) How many records high temperature are less than 109.5? a) 50 b) 40 c) 28 d) يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

45 Stat 110 Ch 2 Using the histogram shown here, do the following : 6. How many values less than 33.5? a) 0 b) 14 c) 10 d) How many classes in the above chart? a) 7 b) 6 c) 12 d) 4 8. The class width is. a) 4 b) 3 c)5 d)2 9. What graph should be used to show the relationship between the parts and the whole? a) Histogram b) Pie graph c) Pareto graph d) Ogives 10. Data collected over period of time can be graphed using..graph a) Pareto graph b) Pie graph c) Time serious d) Curve 24 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

46 Stat 110 Ch Percentages can be used in which type of graph a) Histogram b) Pareto chart c) Pie graph d) Ogive 12. A researcher wishes to represent the percentage of students in the department of statistics using a pie graph. If the percentage of statistical department students is 25%, then their corresponding degree of the angle on the pie graph is... a) 300 b) 1080 c) 900 d) In a stem and leaf plot, the stem part for the data value 347 is... a. 34 b. 7 c. 47 d A department store wants to construct a pie graph to represent the marital status االجت بػ ت) (انحبنت of its employees. There were 30 married, 10 divorced, 20 singles and 5 widows. How many degrees will be needed to represent the divorced( (ان طهقبث employees? a) 41.6⁰ b) 10⁰ c) 55.38⁰ d) 15.4⁰ 25 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

47 Stat 110 Ch When data are collected from January to December in year 2011, then they can be represented by a) Histogram b) Pie graph c) Time series d) Pareto chart 16. The heights of vertical bars in the histogram represent the.. a) Class width b) Sample size c) Frequencies of classes d) Number of classes 26 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

48 Stat 110 Ch 2 Question of chapter : Frequency Distributions and Graphs 1. On a Pareto chart, the frequencies should be represented on the axis a)qualitative B) X C)Y D) quantitative 2. What graph that displays the qualitative data a)pie graph b)pareto chart c) o give D) A and B 3. Data collected over a period of time can be graphed by using a(n).. a)time series b) o give c) Bar graph D)A and B 4. Using the next ogive graph to find the sample size a)pareto chart b)14 c)12 D)16 5. Using the next ogive graph to find how many records are less than 20.5 a)14 b)8 c) 16 D) none of the above 27 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

49 Stat 110 Ch 2 6. Using the next four graphs Which figure is Frequency polygon graph a)4 b)1 c)2 D)3 7. Using the next four graphs Which graph are used to display nominal data a)2 b)1 and 2 c)1 D)3 28 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

50 Stat 110 Ch 2 8. The salaries (in thousands) for 100 employees in IT company are given in this frequency distribution Classes Frequencies The type of the last frequency distribution is, frequency distributions. a)grouped b)continuous c) un grouped D) nominal 9. The salaries (in thousands) for 100 employees in IT company are given in this frequency distribution Classes Frequencies Find the class width a)6 b)8 c)7 D)9 10. The salaries (in thousands) for 100 employees in IT company are given in this frequency distribution Classes Frequencies What are the boundaries for fourth class [ ] [ ] [ ] [ ] 29 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

51 Stat 110 Ch The salaries (in thousands) for 100 employees in IT company are given in this frequency distribution Classes Frequencies The class midpoint for the Second class a)11.5 b) 16.5 c)12.5 D) The lower class limit of the First class a)1.5 b)2 c)2.5 D)9 13. The percentage for the Third class a)0.4% b)4% c) 100% D)40% 14.The cumulative frequency for the Second class a)30 b)10 c)90 D)20 15.Given the following table Classes Frequencies What are the class midpoint for the class limit [17, 24] a)20.5 b)18.5 c)24.5 D) Sample of 56 cars were organized in a frequency distribution according to car brand. If the Nissan class has 8 frequency, what is the degree of it. a)44.43 b)30.43 c)37.43 D ) يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

52 Stat 110 Ch Given the following table Classes Frequencies What is the lower class limit of the class limit [14, 21] a)13.5 b)14 c)14.5 D)21 18.Given the following table Classes Frequencies How many frequencies are less than 39.5 a)42 b)37 c)43 D) Given the following table Classes Frequencies What are the boundaries for the class limit [9, 16] [ ] [ ] [ ] [ ] 19.Data collected over a period of time can be graphed using a...graph. a)time series b) pie c) Bar chart D)patero 20.What are the boundaries for -6 [ ] [ ] [ ] [ ] 31 يح ذ ػ را ر بض بث احصبء نه رحه انجبيؼ /

53 مد م ح عمران حماضرات اون الين زياره الموقع لالستفسار حاله في عدم الرد نرجو ترك رساله باالسم والمادة

54 stat 110 Ch 3 Data description Measures of central tendency Or measures of average هقا س ال ضعة الوشكض ة A statistic A parameter اإلحصائ المعلمة هو مق اس صف خاص ة من خصائص الع نة )sample( هو مق اس صف خاص ة من خصائص المجتمع )population( Type 1-mean (arithmetic average) of measure الوسط الحسابى In most case is not an actual ل س بالضرورة ان كون الوسط الحساب أحد ق م الب انات المعطاة Properties of mean 1) The mean computed by using all the values of a data set 2) The mean for data set is unique and not necessarily of the data value 3) The mean cannot be computed for open- ended frequency distribution 4) The mean is affected by extremely high or low values and may not be the appropriate average الوسط الحساب تأثر بالق م الكب رة جدا وبالق م الصغ رة جدا )الق م الشاذة( For sample x x n For population x n / محمد عمران رياضيات واحصاء للمرحله الجامعيه 1

55 stat 110 Ch 3 Example Find mean for the data 1) Sol Sol / محمد عمران رياضيات واحصاء للمرحله الجامعيه 2

56 stat 110 Ch 3 ال س ط ) (MD Median Median is midpoint of the data array Properties of median 1) The median is used when find the center or middle value of a date must set 2) The median is used when one must determine whether the data values into the upper half or the lower half of the distribution ستخذم ال س ط لتحذ ذ ل الب ا ات تقع ف ال صف العل هي الت ص ع أ ال صف السفل هي الت ص ع 3) The median is used to find the average of an open ended distribution 4) The median is affected less than the mean by extremely high or extremely law value Note When the distribution is extremely skewed the median rather than the mean is more a pproprian measure of central tendency الوس ط اقل تأثرا بالق م الكب ر هاو الق م الصغ رة )الشاذة( من الوسط الحساب قط الو تصف لوجو ع الب ا ات طش ق الحص ل عل ال س ط 1( شتب القشاءات تشت با تصاعذ ا ا ت اصل ا 2( ب ذاء بحزف األ ل هع األخ ش ثن التال هي ا هع التال هي اك إرا تبق عذد احذ ف ال س ط إرا تبق عذد ي ف جوع ن قسو ن عل 2 ال اتج ال س ط / محمد عمران رياضيات واحصاء للمرحله الجامعيه 3

57 stat 110 Ch 3 Example Find median of the data 1)713,300,618,595,311,401,202 Sol الترتيب 202,300,311,401,595,618,713 Median =401 2)684,764,656,702,856,1132,1174,1199 Sol التشت ب 656,684,702,764,856,1132,1174,1199 median / محمد عمران رياضيات واحصاء للمرحله الجامعيه 4

58 stat 110 Ch 3 Mode Mode is the value that occurs most often in a dataset Properties 1) The mode is the only measure of central tendency that can be used when the data are nominal or categorical 2) The mode is not always unique 3) The mode is UN model ف حاله إن المنوال له ق مه واحده 4) The mode is bimodal 5) The mode is multimodal 6) The mode is no mode المنوال ف حاله إن المنوال له ق متان ف حاله إن المنوال له أكثر من ق متان ف حاله انه ال وجد منوال تسمى Example Find the mode of data 1)110,731,1031,84,20,118,1102,1977,103 Sol Mode = no mode 2)8,9,914,8,8,10,7,6,9,7,8,10,11,8,14,11 Sol Mode = 8 unmodel 3)104,104,104,104,104,107,109,109,109,109,109,109,111,111,112 Sol Mode =109 unmodel / محمد عمران رياضيات واحصاء للمرحله الجامعيه 5

59 stat 110 Ch 3 Distribution shapes إشكال التوز عات Symmetric distribution 1) Mean=median=mode التوز ع منتظم 2) Mode median mean ملتو الى ال م ن skewed) positively skewed (right Mean mode = + 3) Mean median mode ملتو الى ال سار skewed) negatively skewed (left Mean mode= / محمد عمران رياضيات واحصاء للمرحله الجامعيه 6

60 stat 110 Ch 3 Example 1) If the mean=median=mode=5, then the distribution is (symmetric) 2) If the mode= 5 and mean=6, then the distribution is (right or positive skewed ) 3) If the mode =5 and the mean = 4. then the distribution (left or negative skewed) The mid rang 1) The mid-range is easy to compute 2) The mid-range gives the mid-point 3) The mid-range is affected by extremely high or low values in data set Mid rang = Example 1) Find the mid rang for the data 2, 3,6,8,4 Sol 2) The values of the median for the values -3,1,-1,-5,-1,-7,1 is a)-1 b)-5 c)1 d)5 sol الترت ب -7,-5,-3,-1,-1,1,1 median is / محمد عمران رياضيات واحصاء للمرحله الجامعيه 7

61 stat 110 Ch 3 3) The raw data set for the stem and leaf plot shown is called a)uni model b)bi model c)multimodal 4) If the number of data set is 7 and it is mean is 8. Then the sum of data values is a) 40 b) 60 c) 80 d) 56 SOL / محمد عمران رياضيات واحصاء للمرحله الجامعيه 8

62 stat 110 Ch 3 5) If the marks of three students are 6, X, 8 and the mean of these marks is 8 then X is a) 8 b) 10 c) 7 d) 9 sol 6) Half of observation are always greater than the a) Median b) mean c) mod d) mid rang 7) Which measure of central tendency are not affected by largely by outliers A) Mid-range and mod b) Median and mod c) Median and mean 8)..is not measure of central tendency a) Mean b) range c) median d) mode 9) A measure obtained from sample data is called a A) Statistic b) population c) parameter 10) What is the term for characteristic measure obtained by using all data values for a specific population? A) Variable b) mode c) statistic d) parametric / محمد عمران رياضيات واحصاء للمرحله الجامعيه 9

63 stat 110 Ch 3 11) If the distribution is symmetric and it is mean equal 10, then the mode equals a) 10 b) 10 c) more than 10 12) If the mode is to the left of the median. And the mean is to the right of the median, then the distribution is a) Symmetric b) right skewed c) left skewed d) negatively skewed 13) The use all data to compute it a) Mean b) range c) mode d) median 14) If each value in a sample has the same frequency, then the data a) Are bimodal b) are multi model C) Have no mode d) are UN model 15) What is the measure of central tendency that appropriate to use when distribution is extremely skewed a) Mean b) median c) mid-range 16) When data are categorize, the most appropriate measure of central tendency? a) Mean b) mode c) median 17) What is the value of the mode, when all values in the data set are different? a) 0 b) 1 c) no mode 18) The symbol for the population mean is A) x b) c) M D d) / محمد عمران رياضيات واحصاء للمرحله الجامعيه 11

64 stat 110 Ch 3 The weight mean w x w x... w nx w w... w 1 2 Where w 1, w 2, w 3,...w n are weight And x 1, x 2, x 3,... x n are values n n = wx w Example 1) A student received an A in English (3 credits).c in statistics (3 credits). a B in physics (4 credit) and a D in mathematics ( 2credits ) assuming A = 4 grade point B = 3grade points C =2 grade points D=1 grades points Find the students grade point average? Sol W X Weight Grade English A 3 4 Stat C 3 2 Phy B 4 3 math D 2 1 ( ( ( ( / محمد عمران رياضيات واحصاء للمرحله الجامعيه 11

65 stat 110 Ch 3 2)an instructor grades exams 20%,term paper 30%,final exam 50% a student has grade of 83,72 and 90 respectively, for exams,term paper and final exam.find the weight mean? Sol W X ( ( ( / محمد عمران رياضيات واحصاء للمرحله الجامعيه 12

66 stat 110 Ch 3 Measure of variation مقا س التشتت Or measure of dispersion (determine the spread of data value) 1)Rang ( R ) R = highest value lowest value 2) Variance and standard deviation For population Variance = = mean 2 X Standard deviation = For sample 2 Variance = s = = x 2 X n X = x X 2 n 1 X = x 2 n X x 2 x 2 n n 1 Standard deviation = S = x X 2 n = x 2 x 2 n n / محمد عمران رياضيات واحصاء للمرحله الجامعيه 13

67 stat 110 Ch 3 3) The coefficient of variation For sample For population c var s = X.100% X = X.100% c var مالحظه هامه إذا كان معامل االختالف لمجتمع ما )أو عيىه( أكبر مه معامل االختالف لمجتمع اخر أو )عيىه أخرى( فان المجتمع األول )العينة األولى( أكثر تغيرا If c var 1 c var 2 Then the first is more variable than second Example If the mean of test A is 70 and it is standard deviation is 7. The mean of test B is 75 and it is standard deviation is 8 which is more variable test A or test B? Sol / محمد عمران رياضيات واحصاء للمرحله الجامعيه 14

68 stat 110 Ch 3 If the variance of the distribution is 16 then the standard deviation of the distribution is a) 16 b) 8 c) 4 d) 1 sol A measure used to compare the variation of two sets of data is called A) Coefficient of variation b) range c) Mean d) Mode Example The number of high way miles per gallon of the ten (10) worst vehicles shown 12,15,13,14,15,16,17,16,17,18 Find 1) Mean 2) median 3) mod 4) mid rage 5) range 6) variance 7) Standard deviation 8) coefficient of variation Sol الترتيب / محمد عمران رياضيات واحصاء للمرحله الجامعيه 15

69 stat 110 Ch 3 ( / محمد عمران رياضيات واحصاء للمرحله الجامعيه 16

70 stat 110 Ch 3 Percentile percential للحصول على p 1 -نرتب االعداد ترت ب تصاعدي ثم نعوض بالقانون التالى (number of value below x total number of value Example A teacher gives a 20-point test to 10 students. The scores are shown here. 18, 15, 12,6,8,2,3,5,20,10 1)Find the percentile of a score 12 Sol التشت ب 2,3,5,6,8,10,12,15,18,20 2) Find the percentile rank for a score 6 Sol / محمد عمران رياضيات واحصاء للمرحله الجامعيه 17

71 stat 110 Ch 3 إذا اعطانا النسبة p وطلب منا الرتبة c نعوض في القانون c n p 100 وإذا كان الناتج عدد نسبى )به فواصل( تقريبه الى اقرب عدد صحيح العدد العدد التالى وإذا كان الناتج عدد صحيح فالرتبة = 2 Example Using the data to get the value that corresponds to the 1)25th percentile Sol ( الىاتج عدد وسبى العذد الز سبت % 25 ستبت العذد الثالث= 5 25th 2)60th percentile Sol عدد صحيح ( 2,3,5,6,8,10,12,15,18, / محمد عمران رياضيات واحصاء للمرحله الجامعيه 18

72 stat 110 Ch 3 Z score or standard score Measures of position مقا س الموضع Z = For sample For population Z = x x s x X Z Score tell how many standard deviation of the data value is above below the mean Ex Z = Find Z score for each test A and test B which is higher Test A X= 38 x = 40 S =50 Test B X=94 x = 100 S= 10 Sol X / محمد عمران رياضيات واحصاء للمرحله الجامعيه 19

73 stat 110 Ch 3 The mean mark in test A is 80 and the standard deviation is 5. If a student get 70 in the test. His relative position (z- score) in the test is a) 6 b) 4 c) 3 sol d)-2 If the mean of a set of data is 24 and 18.4 has a (z-score) = -1.4 then the standard deviation must be a) 8 b) 2 c) 16 d) 4 sol Note 1-if the z score is positive x x 2-if the z- score is zero z=0 x x 3-if the z-score is negative x x / محمد عمران رياضيات واحصاء للمرحله الجامعيه 21

74 stat 110 Ch 3 A box plot Exploratory data analysis استطالع تحل ل الب ا ات 1) The lowest value of the data 2) 3) median 4) 5) the heights value of the data تسو ز الق ن هجو ع الب ا ات Five number summary of the data set Is a median Q 2 Inter quartile rang I Q Q Q R = 3 1 min max 25% 25% 25% 25% Example Construct a box plot for the data 33,38,43,30,29,40,51,27,23,31,42 Sol Min 2 Max / محمد عمران رياضيات واحصاء للمرحله الجامعيه 21

75 stat 110 Ch 3 Find Q, Q, Q for the data set ,13,6,5,12,50,22,18 Sol Find Q, Q, Q for the data set , 18, 22,19,3,21,17,20 Sol / محمد عمران رياضيات واحصاء للمرحله الجامعيه 22

76 stat 110 Ch 3 Outliers 1) Find Q Q 2 Q 2) find I QR Q Q 3) Find Q (1 5 IQR Q (1 5 IQR 4) The low value of Q (1 5 I QR and height value of Q (1 5 IQR called outliers Find outliers for data set 24,32,54,31,16,18,19,14,17,20 Sol Example ( ( ( ( ( ( ( / محمد عمران رياضيات واحصاء للمرحله الجامعيه 23

77 stat 110 Ch 3 All value in a data set are between 6 and 15, expect for one value of 85 the value 85 is likely to be A) The rang b) the box plot c) the mean d) outliers Use the box plot to identify the maximum value, minimum, median, first quartile.third quartile, and interquartile range Sol / محمد عمران رياضيات واحصاء للمرحله الجامعيه 24

78 stat 110 Ch 3 Note box The distribution is approximately symmetric Symmetric 1( إرا كاى ال س ط قش با هي هشكض إل كاى ال س ط إل و ي هشكض إل box The distribution is negatively skewed (left skewed) 2( إرا Left skewed كاى ال س ط إل ساس هشكض إل box The distribution is positively skewed (right skewed) 3( إرا Right skewed / محمد عمران رياضيات واحصاء للمرحله الجامعيه 25

79 stat 110 Ch 3 Use the box plot to indent,, MD, IQR, min value, max value, and show that if this distribution is QQ 1 3 positively or negatively SOL / محمد عمران رياضيات واحصاء للمرحله الجامعيه 26

80 stat 110 Ch 3 Test bank 1- A characteristic or measure obtained by using the data values from a population is called a. A. Statistic B. Quartile C. Percent D. Parameter 2-.. is the symbols of mean in the sample A. B. σ² C. μ D. S² 3- Find the mean of following data 10,15,12,9,2,6? A. 12 B. 9 C. 54 D What is the median of following data 5, 7,10,3,8? A. 7.5 B. 7 C. 6 D If the number of books in a sample of five boxes are follow 11,8,2,2,7,7,2,5. Then the set is said to have A. Multimodal B. Unimodal C. Zero D. No mode / محمد عمران رياضيات واحصاء للمرحله الجامعيه 27

81 stat 110 Ch 3 6-Find the midrange (MR) for the following data 7,-5,2,10,15 A. 2 B. 5 C. -5 D If the mean of 5 values equals 64, then A B. 320 C. 64 D. 200 X? 8-Find the mode for the following data A. 2,3 and 6 B. 2 C. No mode D. 3 and 6 9-The measures of central tendency for the following data 1,3,9,11,2 are: A. Mean=5.2 median=3 mode=no mode B. Mean=6.5 median=9 mode=zero C. Mean=2 median=3 mode=zero D. Mean=5.5 median=10 mode=no mode 10-The cost of four toys in a certain toy shop is given : $15,$20,$32,$1250 Which measure of central tendency should be used? A. Mode B. Mean C. Midrange D. Median / محمد عمران رياضيات واحصاء للمرحله الجامعيه 28

82 stat 110 Ch 3 11-The is a measure of central tendency should be used when the data are qualitative. A. Median B. Range C. Mean D. Mode 12-What is the appropriate measure for the data that represents the marital status (married, divorced, widowed, single) A. Median B. Range C. Mean D. Mode 13-When the distribution is the positive skewed ;the relationship of mean,median and mode will be: A. Mean=Median=Mode B. Mean>Median>Mode C. Mean<Median<Mode D. The exact relationship cannot be determined 14-Find the mean and sample standard deviation for the following data set: 10, 5, 15, 20, 30, (Hint: x ). A) mean= 16, standard deviation= B) mean= 16, standard deviation= 9.62 C) mean= 16, standard deviation= 92.5 D) mean= 16, standard deviation= If a sample size is 9 and the standard deviation 7 then the variance is: A. 49 B. 2.6 C. 2 D محمد عمران رياضيات واحصاء للمرحله الجامعيه /

83 stat 110 Ch 3 16-If the Cvar for English final examination was 6.9% and Cvar for History final examination was 4.9%. Compare The variations. A. The English class was more variable B. The History class was more variable C. Both of classes has the same variation D. Cannot determined 17-The mean of the number of sales of houses over a 3-month period is 56, and variance is 36, then the coefficient of variation is : A. 10.7% B % C. 64.3% D % 18-When a distribution is bell-shaped, approximately what percentage of data values will fall within 1, standard deviation of the mean? A. 95% B % C. 68% D. 99.7% 19-The mean of a distribution is 80 and the standard deviation is 7, if the distribution is normal, then approximately99.7% of the data will fall between A. 50 and 80 B. 59 and 101 C. 66 and 94 D. 73 and / محمد عمران رياضيات واحصاء للمرحله الجامعيه 31

84 stat 110 Ch 3 20-The data value that is smaller than Q1 1.5 A) Minimum B) Median C) Quartile D) Outlier IQR 21-From the box plot below which class is more variable: Class A, is said to be: Class B A) Both class are the same B) Class A is more variable than class B C) Class B is more variable than class A D) Cannot be determined 22-Find the Z-score for the value75,when the mean is 80 and the standard deviation is 5 A. Z= B. Z= -1 C. Z= 1 D. Z= Which is not part a five-number summary? A. The mean B. The median C. The smallest and the largest data values D. and / محمد عمران رياضيات واحصاء للمرحله الجامعيه 31

85 stat 110 Ch 3 *Use the following boxplot graph to answer questions(24-26) IQR is approximately: A. 60 B. 0 C. 80 D The distribution shape is : A. Negative skewed B. Symmetrical C. Left skewed D. Positive skewed 26-The minimum value is A. 30 B. 10 C. 90 D / محمد عمران رياضيات واحصاء للمرحله الجامعيه 32

86 stat 110 Ch 3 Question of chapter : Data Description 1. The largest value is possible to the non-outlier values for the data is shown in the next boxplot, a)13 b)12.5 c)13.5 D)12 2. The difference between a S 2 and a σ 2 is due to a)standard error of the mean c)sampling error b)sampling distribution D) no answer 3. if the majority of the data values fall to the right of the mean, then the distribution is skewed. a)negatively b)symmetric c) no answer D)positively 4. The mean of the waiting time in an emergency room is 78.2 minutes with a standard deviation of 13 minutes for people who are admitted for additional treatment. The mean of the waiting time for patients who are discharged after receiving treatment is minutes with a standard deviation of 18.6 minutes. Which waiting time are more variable? a)we cannot determine b) the two waiting time have same variable c)the waiting time patients who are discharged after receiving treatment are more variable D)the waiting time in an emergency more variable / محمد عمران رياضيات واحصاء للمرحله الجامعيه 33

87 stat 110 Ch 3 5. is an extremely high or an extremely low data value when compared with the rest of the data values. a)percentiles b) an outliers c)there is no answer D) A Z score 6. Using the grades X 1, X 2, X 3, X 4, X 5, X 6, X 7, where X 1 < X 2 < X 3 < X 4 < X 5 < X 6 < X 7 to find the percentile rank of a grade of X 4 a)53th b)50 th c)52th D)46th 7. Given this boxplot The maximum value is a)10 b)12 c)13 D)11 8. The value corresponding to the 25th percentile is a)6 b) 5 c)4 D)7 9. The average score on a state CDL license exam is 75 with a standard deviation of 6. Find the corresponding z score for score 63. a)-5 b)0 c) -2 D) / محمد عمران رياضيات واحصاء للمرحله الجامعيه 34

88 stat 110 Ch Which has a better relative position: a score of 66 on an English test with a mean of 56 and a standard deviation of 18 or a score of 33 on an Arabic test with a mean of 28 and standard deviation of 9? a)a score of English test is better than a score of Arabic test b) A score of Arabic test is better than score of English test c) the two score are the same D) we cannot determine , 44, 12, 26, 36, 7 The Q 2 = a)19 b) 26 c)22.5 D) , 18, 26, 37, 10, 47 The Q 1 = a)5 b)18 c)26 D) , 13, 18, 4, 29, 36 The Q 3 = a)36 b)46 c)18 D) / محمد عمران رياضيات واحصاء للمرحله الجامعيه 35

89 stat 110 Ch , 30, 36, 14, 19, 48 The IQR = a)19 b)20 c)22 D ) / محمد عمران رياضيات واحصاء للمرحله الجامعيه 36

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