Higher Secondary - First year STATISTICS Practical Book
|
|
- Rudolph Boyd
- 5 years ago
- Views:
Transcription
1 Higher Secondary - First year STATISTICS Practical Book th_statistics_practicals.indd :00:9
2 Introduction Statistical tools are important for us in daily life. They are used in the analysis of data pertaining to various activities such as production, consumption, distribution, banking and insurance, trade, transport, etc. Practical work also gives students many opportunities to use their minds to adopt suitable statistical tools and methods on various types of analysis for the given sample data. Objectives It facilitates comparison with similar data. Tabulation of data Compares the tabular data with diagrammatic representation of data Represents the data in a graph Presents the data in suitable diagrams Distinguishes diagrammatic and graphical representation of data Calculates the mathematical averages and the positional averages Computes quartiles, Deciles, Percentiles and interprets Measures the spread or dispersion Understands the theorems on probability and applies in problems Measures the Skewness Fittings Binomial and poisson distribution Instructions To Students Students must attend all the practical classes. They must also remember that there is a great degree of co-ordination between theory problems and practical problems. The following are some of the items that they must bring to the Practical Classes. Practical observation note book Practical record Pencil sharpener Eraser A measuring scale Graph sheets Compass and protractor Calculator th standard Statistics Practical Come prepared with theory part of the practical subject. They should submit the practical records periodically for correction and evaluation. They must maintain strict discipline and silence in the statistical laboratory. They should write the date and experiment number in their observation note books. th_statistics_practicals.indd :00:9
3 Students must answer any three out of five questions from the following topics. Formation of Frequency Table. Diagrammatic Representation of data. Graphical Representation of data 4. Measures of Central Tendency 5. Measures of Dispersion 6. Measures of Skewness 7. Simple problem in probability 8. Probability Mass Function and Probability Density Function 9. Computation of Mean and Variance for Random Variables 0. Fitting Binomial Distribution. Fitting Poisson Distribution MODEL QUESTION PAPER I Marks 5 Duration: ½ hrs. Answer any three of the following Construct a stem and leaf plot for the following and find range, Median and Mode.., 0.7, 0.9,.44,.0, 0.88, 0.99, 0.7, 0.9, 0.98,., 0.79,.4,.9,.08, 0.94,.06,.,.0.. Administration of a school wished to initiate suitable preventive measures against breakage of equipments in its chemistry laboratory. Information collected about breakage of equipment occurred during the year 07 in the laboratory are given below. Equipments Burette Conical flask Test tube Pipette No. of Breakages Draw pareto diagram for the above data. Which equipment requires more attention in order to reduce breakages?. Find the Q, Q, D 7, of the frequency distribution given below. Marks in Statistics < > 70 Number of students Given three identical boxes I, II and III containing two coins. In Box I both coins are gold coin, in Box II both are silver coin, in Box III there is one gold and one silver coin. A person chooses a box at random and takes out a coin if the coin is gold what is the probability that the other coin in the box is also gold? 5. A set of 4 coins are tossed 64 times. The number of occurrences of head is tabulated as follows. Number of Heads 0 4 Number of times Fit a Binomial distribution for the foresaid data and find the expected frequencies. th_statistics_practicals.indd :00:9
4 ANSWERS FOR MODEL QUESTION PAPER - I. Aim: To construct a stem and leaf plot and finding the values of range, Median and Mode. Formula: Calculation: Range : L S Median : Mid value of the data Mode : Term occurring most frequently Write the numbers in ascending order 0.7, 0.7, 0.79, 0.88, 0.9, 0.9, 0.94, 0.98, 0.99,.0,.0,.06,.08,.,.,.4,.9,.,.9,.44. Stem Leaf 0.7,, ,, 4, 8,9.0,, 6, 8.,, 4, Range: Median: [From the stem and leaf plot, the lowest and highest value can be found out easily] Highest value (L).44, Lowest value (S) 0.7 Range L - S th 0 item + th item Mode: 0.9 Result: Range 0.7 Median.0 Mode th_statistics_practicals.indd :00:4
5 . Aim: To draw a pareto diagram. Given: Formula: Calculation: Equipment Data To find percentage value total 00 Arrange the given data in descending order of frequency. No. of Breakages (f) Test tube 50 Conical flask 75 Burette 45 Pipette 0 Number of Breakages in percentage Total Cumulative percentage No of breakages in the chemistry laboratory Y 75% 90% 00% Y axis : unit 0 breakages No. breakages % Tt Test tube Cf Conical flask Bu Burette Pi Pipette 0 0 Tt Cf Bu Pi Equipment X Result: 50% of breakage is due to test tube and 5% is due to conical flask. i. Pareto diagram is drawn ii. The school administration has to focus more attention on reducing the breakages of test tubes and conical flasks. 5 th_statistics_practicals.indd :00:46
6 . Aim: To find Q, Q and D 7 Formula: Q l+ N 4 m c f Q N m l+ 4 c f D Calculations: 7 l+ 7N m 0 c f To find Q and Q Marks in Statistics No. of Students f Cumulative frequency Below (m) 0-0 (l) 0 f (m) (l) 8 f Above N N m Q l+ 4 c f l 0, N 6. 5, f 0 m 0 c Q N th_statistics_practicals.indd :00:58
7 Q l+ N m 4 c f l 50, N , f 8 m 0 c Q N N m D7 l+ 0 c f l 50, 7N 0 0., f 8 m 0 c D Result: Q 8.5, Q 5.68, D Aim: To find the probability by using Baye s theorem Formula: P E A Calculation: P( E ) P( A E ) i P E P A E i i E, E and E be the events that the boxes I, II, III are chosen respectively. P ( E) P ( E) P ( E ) Let A be the event that the gold coin is drawn P ( A E ) 0 P ( A E ) 0 P ( A E ) 7 th_statistics_practicals.indd :0:8
8 P ( E A) Result: Probability that the second coin in the box is gold is /. 5. Aim: To fit a Binomial distribution Formula: (i) x f x N (ii) x p, q p n (iii) x n x p ( x) nc p q, x 0,... n (iv) (v) F ( 0) N p( 0) x n x p F( x+ ) F x x + q Calculation: n 4 6 (i) x 64 (ii). 5 x f f x Total 64 6 x p n q p th_statistics_practicals.indd :0:
9 (iii) x 4 x x p x 4c , x 0,... 4 ( 0) 4 c ( 05. ) ( 0. 47) (iv) F 0 N p 0 (v) p ( 047. ) F ( 0) n x p F( x+ ) F x x + q When x F( 0+ ) F F() When x F ( + ) F () F When x 4 05 F ( + ) F F When x F ( + ) F F ( 4) Result: (i) (ii) The fitted binomial distribution is x 4 x x P X x 4c , x 0,,, The Expected frequencies are x 0 4 Observed frequencies Expected frequencies th_statistics_practicals.indd :0:5
10 MODEL QUESTION PAPER II Marks 5 Duration: ½ hrs. Answer any three of the following The number of hours spent by a School Student on Various activities on a working day, is given below. Construct a pie chart using the angle measurement. Activity Sleep School Play Homework Others Number of hours Draw a pie chart to represent the above information.. The following is the distribution of marks obtained by 09 Students in a Subject in an institution. Find the Geometric mean. Marks No of Students The wholesale price of a commodity for seven consecutive days in a month is a follows. Days Commodity/Price/Quintal Find varance and standard deviation 4. A number is selected randomly from the digits through 9. Consider the events. A {, 4, 6, 8, 9}, B {, 4, 8, 9}, C {, 5, 8, 9} Find (i) P (A/B) (ii) P (A/C) (iii) P (B/C) (iv) P (B/A) 5. The p.d.f of a continuous random variable X is given by x, 0 < x < f ( x) find its mean and variance. 0, elsewhere 0 th_statistics_practicals.indd :0:5
11 ANSWERS FOR MODEL QUESTION PAPER II. Aim: Construct a pie chart using the angle measurement Formula: Calculation: The central angle of a Component is [value of the Component/Total value] 60 0 Activity Duration in hours Central angle Sleep 8 School 6 Play Homework Others Total Homework 45 Play 45 Sleep 0 Others 60 School 90 th_statistics_practicals.indd :0:58
12 . Aim: To find the Geometric mean. Formula: Calculation: GM. Anti log n i f i N log xi Marks Midpoint (x i ) f i log x i f i log x i Total N GM. Anti log n i fi log xi N Anti log 09 GM Anti log [. 587] Result: Geometric mean marks of 09 students in a subject is 8.4. Aim: To find the variance and standard deviation Formula: d Variance d n n Standard deviation var iance th_statistics_practicals.indd :0:04
13 Calculation: Standard deviation Observations d x - A d d Variance d n n var iance Result: Variance 06 Standard deviation Aim: To find the conditional probability Formula: P A B P A C P B C P B A P( B) ( C) PC ( C) PC ( A) P( A) P A B P A P B P B th_statistics_practicals.indd :0:
14 Calculation: A {, 4, 6, 8, 9}, B {, 4, 8, 9}, C {, 5, 8, 9} A B{ 4, 8, 9} A C { 8, 9} B C 5 4 P( A) P( B) 9 9 P( A B) P( A C) 9 9 P B C The probability for the occurrence of A given that B has occurred is P A P A B ( B) 9 P( B) 4 9 P( A B) 4 The probability for the occurrence A given that C has occurred is P A P A C ( C) 9 PC 4 9 P( A C) 4 Similarly the Conditional Probability of B given C P B P B C ( C) 9 PC 4 9 P( B C) The Conditional probability of B given A is P B P B A ( A) 9 P( A) 5 9 P( B A) 5 Result: P( A B) 4 P( A C) 4 P( B C) P( B A) 5 5. Aim: To find mean and variance Formula: E X x f x dx E X x f x dx Variance X E X E X 4 th_statistics_practicals.indd :0:7
15 Calculation: x E( X) x dx 0 x 0 x dx E( X ) 0 x x dx x dx 0 4 x Variance X E X E X Result: 9 Mean E (X) 4 Variance (X) /9 5 th_statistics_practicals.indd :0:5
16 MODEL QUESTION PAPER III STATISTICS PRACTICAL Marks 5 Duration: ½ hrs. Answer any three of the following Construct a bi-variate frequency distribution table for the following data of twenty students. Marks in Economics Marks in Statistics Find the measures of central tendencies for the following data. Wages ( ) No of labourers Draw Box - Whisker plot for the following, 5, 0,,, 0,, 9, 7, 7, 6 4. Two coins are tossed one by one. First throw is considered as X and second throw is considered as Y. The joint probability distribution of X and Y is given by X Y Verify E ( XY) E( X) E( Y ) 5. The following mistakes per page were observed in a book Number of mistakes (per page) 0 4 Number of pages Fit a poisson distribution and estimate the expected frequencies. 6 th_statistics_practicals.indd :0:54
17 . Aim: ANSWERS MODEL QUESTION PAPER III To construct a bi-variate frequency distribution. Calculation Let X denote marks in Economics Y denote marks in Statistics Eco/Stat l ll ll l l - 4 l l l lll lll l 4-6 ll l Frequency Distribution Table X/Y Total Total Aim: To find the measures of central tendencies Formula: Calculation n fi xi i x N, x i is the midpoint of the class interval. Median l + N m C f f f0 Mode l + f f f 0 C Wages No of labourers (f) Mid value x f x N 4 fx845 A.M f x x N th_statistics_practicals.indd :0:0
18 Median No of labourers Cumulative Wages (f) frequency N 4 N 4. 5 f 0, m 5, l 40, N. 5, C 0 l + Median Mode N m C f Wages No of labourers (f) f 0, f 0, l 40, f 5, c 0 0 f f0 Mode l + f f f 0 c 8 th_statistics_practicals.indd :0:0
19 Result : Measures of Central tendencies Arithmetic mean x 4. 9 Median 4.5 Mode 44. Aim: Draw box- whisker plot. Formula Calculation : Q Q Q n + 4 th n + th n + 4 item th item item First arrange in the ascending order,5,0,,,6,7,7,9,0, n Q n + 4 th item Q th rd item Q 0 th item item 9 th_statistics_practicals.indd :0:
20 Q n + th th + th 6 item Q 6 th. item item item Q n th 9 th item Q 9. th th item item item Minimum Value and Maximum Value L Q 0 Q 6 Q 9 H L Q 0 Q 6 Q 9 H L Q 0 Q 9 H Result: Q 6 Box- Whisker plot is drawn using Five number summary. 0 th_statistics_practicals.indd :0:4
21 4. Aim To Verify E( xy) E( x) E( y) Formula x y P E xy xy j i i j ij XY 0 Total Total Calculation: E ( x) E y x P i i i yp j j j A random variable x, y can table the values o and E( xy) P ( xi yj) x y i j i j x x E x i x p x E y j i j i yp X0.5+0X E( xy) E( y) E( xy) E( x) E( y) Result: E( xy) E( x) E( y) is verified 5. Aim To fit a Poisson distribution and estimate the expected frequencies Formula i) x fx ii) x iii) P( x) f e x x! th_statistics_practicals.indd :0:
22 o iv) P e ( 0) e 0! v) F 0 N P 0 vi) F x ( + ) F( x) x + i) Mean x f fx Total 5 4 iii) P x x e x! fx x f 4 5 x e ( 044. ) x! x ii) x e ( 044. ) 044. iv) P( 0) e ! v) F 0 N P vi) F x ( + ) F( x) x + F F F F Result: F () ( + ) F( ) F( ) F( ) Fitted Poisson distribution is x e 044. P( x x), x 0,,... x! Expected Frequencies are given below x 0 4 Total Observed frequency Expected frequency th_statistics_practicals.indd :0:44
23 MODEL QUESTION PAPER IV STATISTICS PRACTICAL Marks 5 Duration: ½ hrs. Answer any three of the following Draw more than ogive curve for the following data showing the marks secured by the students of class XI in a school. Marks No of students a) Estimate the total number of students who secured marks more than. b) Find the median of the data. (i) From the known data, mean 7.5, mode 8 and variance.69 then find the karl peasson coefficient of skewness. (ii) If Q 40 Q 50,Q 60 find Bocoleys Coefficient of skewness. ) A Question Paper contains section A with 5 Questions and section B with 7 Questions. A Student is required to attempted 8 Questions in all, Selecting at least from each section. In how many ways can a student select the Question? 4) A discrete random variable has the following distribution function. x P( x) a a 5a 7a 9a a a 5a 7a Find (i) a (ii) P( x< ) (iii) P( x ) 5 (iv) P < x< 7 5. Student of a class were given an aptitude test. Their marks were found to he normally distributed with mean 60 and the standard deviation 5. What Percentage of students scored (i) more than 60 marks (ii) less than 56 marks (iii) between 45 and 65 marks. th_statistics_practicals.indd :0:48
24 ANSWERS MODEL QUESTION PAPER IV. Aim To find the median of the data by using ogive curve Calculation. More then ogive More than ogive Less than ogive Marks less than No of students Marks greater than No of students No of students Median 0 0 x x Marks Result: a) The total number of students who secured marks more than 6 students b) Median 6 4 th_statistics_practicals.indd :0:48
25 . Aim To find the coefficient of skewness Given data (i) mean 7.5, Mode 8, variance.69 (ii) Q 40 Q 50 Q 60 Formula: (i) Karl Pearson coefficient of skewness Mean mod e S tan darddeviation Q + Q Q (i) Bowler s Coefficient of skewness Q Q Calculation: (i) Karl Pearson coefficient of skweness Standard deviation var iance Coeff.of skweness ii) Bowley s coefficient of skewness Given distribution is symmetric Result: (i) Karl Pearson Coefficient of skewness -0.5 (ii) Bowley s coefficient of skewness 0 and hence the distribution is symmetric. 5 th_statistics_practicals.indd :0:5
26 . Aim To find the number of ways selecting the question Given data Section No. of questions A 5 B 7 Calculation: To select at least questions from each section to take totally 8 questions. Section Number of Selections A (5) 4 B(7) 5 4 Combinations C 7C C C4 C C C5 7C 5 Total number of selection is Result: Number of ways selection 8 questions from section A and B is Aim To find a and their probabilities Calculation Since P( x x) is probability mars function P x x P( x 0)+ P( x ) P( x )+ P( x )+ P( x 4)+ P( x 5)+ P( x 6)+ P( x 7)+ P( x 8) a+ a + 5a + 7a + 9a + a + a + 5a + 7a 8a a 8 (ii) P( x< ) P( x o) + p( X )+ p X a+ a + 5a 6 th_statistics_practicals.indd :0:57
27 9 8 (iii) P( x 5) P( x 5) + P( x 6)+ P( x 7) + P x 8 a + a 5a + 7a 56 8 ( ) + ( ) + ( ) (iv) P < x< 7 P x 4 P x 5 P x 6 Result 9a + a + a 8 (i) a 8 (iv) P x 7 < < 8 (ii) P( x< ) 9 8 (iii) P( x 5) Aim : To find the percentage of students scoring more than / less than particular marks using normal distribution Given data 60, 5 Formula (i) x (ii) Standard normal table Calculation: (i) more than 60 marks P( x> 60) Pz ( > ) 5 p( z > 0) P 0 < z < Percentage of students scoring more than 60 marks % 7 th_statistics_practicals.indd :04:0
28 - z 0 (ii) Less than 56 marks P x< Pz ( < ) 5 P z < 08. P( < z < 0) P 0. 8< z < P( 0< z < 08. ) Percentage of students scored less than 56 marks 0.9x00.9% - z -8 z 0 (ii) Between 45 and 65 marks P( 45 < x< 65) P < z< 5 5 P < z < P( < z < 0)+ P 0< z < Percentage of students scored marks between 45 and 65 is 0.899x008.99% - z z 0 z Result (i) Percentage of students scored more than 60 marks 50% (ii) Percentage of students scored less than 56 marks.9% (iii) Percentage of students scored marks between 45 and 65 is 8.99% 8 th_statistics_practicals.indd :04:08
Class 11 Maths Chapter 15. Statistics
1 P a g e Class 11 Maths Chapter 15. Statistics Statistics is the Science of collection, organization, presentation, analysis and interpretation of the numerical data. Useful Terms 1. Limit of the Class
More informationadditionalmathematicsstatisticsadditi onalmathematicsstatisticsadditionalm athematicsstatisticsadditionalmathem aticsstatisticsadditionalmathematicsst
additionalmathematicsstatisticsadditi onalmathematicsstatisticsadditionalm athematicsstatisticsadditionalmathem aticsstatisticsadditionalmathematicsst STATISTICS atisticsadditionalmathematicsstatistic
More informationMIDTERM EXAMINATION (Spring 2011) STA301- Statistics and Probability
STA301- Statistics and Probability Solved MCQS From Midterm Papers March 19,2012 MC100401285 Moaaz.pk@gmail.com Mc100401285@gmail.com PSMD01 MIDTERM EXAMINATION (Spring 2011) STA301- Statistics and Probability
More informationOverview of Dispersion. Standard. Deviation
15.30 STATISTICS UNIT II: DISPERSION After reading this chapter, students will be able to understand: LEARNING OBJECTIVES To understand different measures of Dispersion i.e Range, Quartile Deviation, Mean
More informationTOPIC: Descriptive Statistics Single Variable
TOPIC: Descriptive Statistics Single Variable I. Numerical data summary measurements A. Measures of Location. Measures of central tendency Mean; Median; Mode. Quantiles - measures of noncentral tendency
More informationCIVL 7012/8012. Collection and Analysis of Information
CIVL 7012/8012 Collection and Analysis of Information Uncertainty in Engineering Statistics deals with the collection and analysis of data to solve real-world problems. Uncertainty is inherent in all real
More informationPostal Test Paper_P4_Foundation_Syllabus 2016_Set 1 Paper 4 - Fundamentals of Business Mathematics and Statistics
Paper 4 - Fundamentals of Business Mathematics and Statistics Academics Department, The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament) Page 1 Paper 2 - Fundamentals
More informationUnit 2. Describing Data: Numerical
Unit 2 Describing Data: Numerical Describing Data Numerically Describing Data Numerically Central Tendency Arithmetic Mean Median Mode Variation Range Interquartile Range Variance Standard Deviation Coefficient
More informationDr. Babasaheb Ambedkar Marathwada University, Aurangabad. Syllabus at the F.Y. B.Sc. / B.A. In Statistics
Dr. Babasaheb Ambedkar Marathwada University, Aurangabad Syllabus at the F.Y. B.Sc. / B.A. In Statistics With effect from the academic year 2009-2010 Class Semester Title of Paper Paper Per week Total
More informationChapter 3. Data Description
Chapter 3. Data Description Graphical Methods Pie chart It is used to display the percentage of the total number of measurements falling into each of the categories of the variable by partition a circle.
More informationFinal Exam STAT On a Pareto chart, the frequency should be represented on the A) X-axis B) regression C) Y-axis D) none of the above
King Abdul Aziz University Faculty of Sciences Statistics Department Final Exam STAT 0 First Term 49-430 A 40 Name No ID: Section: You have 40 questions in 9 pages. You have 90 minutes to solve the exam.
More informationPSYCHOLOGICAL STATISTICS
PSYCHOLOGICAL STATISTICS B Sc. Counselling Psychology 011 Admission onwards II SEMESTER COMPLIMETARY COURSE UIVERSITY OF CALICUT SCHOOL OF DISTACE EDUCATIO CALICUT UIVERSITY.P.O., MALAPPURAM, KERALA, IDIA
More informationIAM 530 ELEMENTS OF PROBABILITY AND STATISTICS LECTURE 3-RANDOM VARIABLES
IAM 530 ELEMENTS OF PROBABILITY AND STATISTICS LECTURE 3-RANDOM VARIABLES VARIABLE Studying the behavior of random variables, and more importantly functions of random variables is essential for both the
More informationP8130: Biostatistical Methods I
P8130: Biostatistical Methods I Lecture 2: Descriptive Statistics Cody Chiuzan, PhD Department of Biostatistics Mailman School of Public Health (MSPH) Lecture 1: Recap Intro to Biostatistics Types of Data
More informationEXAM. Exam #1. Math 3342 Summer II, July 21, 2000 ANSWERS
EXAM Exam # Math 3342 Summer II, 2 July 2, 2 ANSWERS i pts. Problem. Consider the following data: 7, 8, 9, 2,, 7, 2, 3. Find the first quartile, the median, and the third quartile. Make a box and whisker
More informationCounting principles, including permutations and combinations.
1 Counting principles, including permutations and combinations. The binomial theorem: expansion of a + b n, n ε N. THE PRODUCT RULE If there are m different ways of performing an operation and for each
More information384 PU M.Sc Five year Integrated M.Sc Programmed (Mathematics, Computer Science,Statistics)
384 PU M.Sc Five year Integrated M.Sc Programmed (Mathematics, Computer Science,Statistics) 1 of 1 146 PU_216_384_E 2 cos 1 π 4 cos 1 cos1 2 of 1 15 PU_216_384_E 1! 1 1 3 of 1 15 PU_216_384_E 1 4 of 1
More informationMIT Arts, Commerce and Science College, Alandi, Pune DEPARTMENT OF STATISTICS. Question Bank. Statistical Methods-I
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 MIT Arts, Commerce and Science College, Alandi, Pune DEPARTMENT OF STATISTICS Question Bank Statistical Methods-I Questions for 2 marks Define the following terms: a. Class limits
More information1.0 Continuous Distributions. 5.0 Shapes of Distributions. 6.0 The Normal Curve. 7.0 Discrete Distributions. 8.0 Tolerances. 11.
Chapter 4 Statistics 45 CHAPTER 4 BASIC QUALITY CONCEPTS 1.0 Continuous Distributions.0 Measures of Central Tendency 3.0 Measures of Spread or Dispersion 4.0 Histograms and Frequency Distributions 5.0
More information2011 Pearson Education, Inc
Statistics for Business and Economics Chapter 2 Methods for Describing Sets of Data Summary of Central Tendency Measures Measure Formula Description Mean x i / n Balance Point Median ( n +1) Middle Value
More informationA is one of the categories into which qualitative data can be classified.
Chapter 2 Methods for Describing Sets of Data 2.1 Describing qualitative data Recall qualitative data: non-numerical or categorical data Basic definitions: A is one of the categories into which qualitative
More informationCHAPTER 1. Introduction
CHAPTER 1 Introduction Engineers and scientists are constantly exposed to collections of facts, or data. The discipline of statistics provides methods for organizing and summarizing data, and for drawing
More information1. Exploratory Data Analysis
1. Exploratory Data Analysis 1.1 Methods of Displaying Data A visual display aids understanding and can highlight features which may be worth exploring more formally. Displays should have impact and be
More informationMIDTERM EXAMINATION STA301- Statistics and Probability (Session - 4) Question No: 1 (Marks: 1) - Please choose one 10! =. 362880 3628800 362280 362800 Question No: 2 (Marks: 1) - Please choose one If a
More informationObjective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode.
Chapter 3 Numerically Summarizing Data Chapter 3.1 Measures of Central Tendency Objective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode. A1. Mean The
More informationChapter 7: Statistics Describing Data. Chapter 7: Statistics Describing Data 1 / 27
Chapter 7: Statistics Describing Data Chapter 7: Statistics Describing Data 1 / 27 Categorical Data Four ways to display categorical data: 1 Frequency and Relative Frequency Table 2 Bar graph (Pareto chart)
More informationF78SC2 Notes 2 RJRC. If the interest rate is 5%, we substitute x = 0.05 in the formula. This gives
F78SC2 Notes 2 RJRC Algebra It is useful to use letters to represent numbers. We can use the rules of arithmetic to manipulate the formula and just substitute in the numbers at the end. Example: 100 invested
More informationQuantitative Methods Chapter 0: Review of Basic Concepts 0.1 Business Applications (II) 0.2 Business Applications (III)
Quantitative Methods Chapter 0: Review of Basic Concepts 0.1 Business Applications (II) 0.1.1 Simple Interest 0.2 Business Applications (III) 0.2.1 Expenses Involved in Buying a Car 0.2.2 Expenses Involved
More informationIntroduction to Statistics
Introduction to Statistics Data and Statistics Data consists of information coming from observations, counts, measurements, or responses. Statistics is the science of collecting, organizing, analyzing,
More informationAfter completing this chapter, you should be able to:
Chapter 2 Descriptive Statistics Chapter Goals After completing this chapter, you should be able to: Compute and interpret the mean, median, and mode for a set of data Find the range, variance, standard
More informationINTENDED LEARNING OUTCOMES At the completion of this course, students are expected to:
EDO UNIVERSITY IYAMHO COURSE CODE: ECO 113 COURSE TITLE: Introductory Statistics 1 NUMBER OF UNITS:2 Units COURSE DURATION: Two hours per week COURSE LECTURER: Dr. Sylvester Ohiomu INTENDED LEARNING OUTCOMES
More informationMTH001- Elementary Mathematics Solved Final Term Papers For Final Term Exam Preparation
MTH001- Elementary Mathematics Solved Final Term Papers For Final Term Exam Preparation Question No: 1 The difference between the upper and the lower class boundaries of a class are known as: Class Marks
More informationLearning Objectives for Stat 225
Learning Objectives for Stat 225 08/20/12 Introduction to Probability: Get some general ideas about probability, and learn how to use sample space to compute the probability of a specific event. Set Theory:
More informationLC OL - Statistics. Types of Data
LC OL - Statistics Types of Data Question 1 Characterise each of the following variables as numerical or categorical. In each case, list any three possible values for the variable. (i) Eye colours in a
More informationStatistics 1. Edexcel Notes S1. Mathematical Model. A mathematical model is a simplification of a real world problem.
Statistics 1 Mathematical Model A mathematical model is a simplification of a real world problem. 1. A real world problem is observed. 2. A mathematical model is thought up. 3. The model is used to make
More informationAuthor : Dr. Pushpinder Kaur. Educational Statistics: Mean Median and Mode
B.ED. PART- II ACADEMIC SESSION : 2017-2018 PAPER XVIII Assessment for Learning Lesson No. 8 Author : Dr. Pushpinder Kaur Educational Statistics: Mean Median and Mode MEAN : The mean is the average value
More information21 ST CENTURY LEARNING CURRICULUM FRAMEWORK PERFORMANCE RUBRICS FOR MATHEMATICS PRE-CALCULUS
21 ST CENTURY LEARNING CURRICULUM FRAMEWORK PERFORMANCE RUBRICS FOR MATHEMATICS PRE-CALCULUS Table of Contents Functions... 2 Polynomials and Rational Functions... 3 Exponential Functions... 4 Logarithmic
More informationBOARD QUESTION PAPER : JULY 2017 ALGEBRA
BOARD QUESTION PAPER : JULY 017 ALGEBRA Time : Hours Total Marks : 40 Note: (i) (ii) All questions are compulsory. Use of calculator is not allowed. Q.1 Attempt any five of the following sub - questions
More informationLecture Notes for BUSINESS STATISTICS - BMGT 571. Chapters 1 through 6. Professor Ahmadi, Ph.D. Department of Management
Lecture Notes for BUSINESS STATISTICS - BMGT 571 Chapters 1 through 6 Professor Ahmadi, Ph.D. Department of Management Revised May 005 Glossary of Terms: Statistics Chapter 1 Data Data Set Elements Variable
More informationUniversity of Jordan Fall 2009/2010 Department of Mathematics
handouts Part 1 (Chapter 1 - Chapter 5) University of Jordan Fall 009/010 Department of Mathematics Chapter 1 Introduction to Introduction; Some Basic Concepts Statistics is a science related to making
More informationGlossary. The ISI glossary of statistical terms provides definitions in a number of different languages:
Glossary The ISI glossary of statistical terms provides definitions in a number of different languages: http://isi.cbs.nl/glossary/index.htm Adjusted r 2 Adjusted R squared measures the proportion of the
More informationMeasures of Central Tendency
Measures of Central Tendency Summary Measures Summary Measures Central Tendency Mean Median Mode Quartile Range Variance Variation Coefficient of Variation Standard Deviation Measures of Central Tendency
More informationExample 2. Given the data below, complete the chart:
Statistics 2035 Quiz 1 Solutions Example 1. 2 64 150 150 2 128 150 2 256 150 8 8 Example 2. Given the data below, complete the chart: 52.4, 68.1, 66.5, 75.0, 60.5, 78.8, 63.5, 48.9, 81.3 n=9 The data is
More informationReview for Exam #1. Chapter 1. The Nature of Data. Definitions. Population. Sample. Quantitative data. Qualitative (attribute) data
Review for Exam #1 1 Chapter 1 Population the complete collection of elements (scores, people, measurements, etc.) to be studied Sample a subcollection of elements drawn from a population 11 The Nature
More informationRaquel Prado. Name: Department of Applied Mathematics and Statistics AMS-131. Spring 2010
Raquel Prado Name: Department of Applied Mathematics and Statistics AMS-131. Spring 2010 Final Exam (Type B) The midterm is closed-book, you are only allowed to use one page of notes and a calculator.
More informationTypes of Information. Topic 2 - Descriptive Statistics. Examples. Sample and Sample Size. Background Reading. Variables classified as STAT 511
Topic 2 - Descriptive Statistics STAT 511 Professor Bruce Craig Types of Information Variables classified as Categorical (qualitative) - variable classifies individual into one of several groups or categories
More informationEssentials of Statistics and Probability
May 22, 2007 Department of Statistics, NC State University dbsharma@ncsu.edu SAMSI Undergrad Workshop Overview Practical Statistical Thinking Introduction Data and Distributions Variables and Distributions
More informationSTATISTICS. 1. Measures of Central Tendency
STATISTICS 1. Measures o Central Tendency Mode, median and mean For a sample o discrete data, the mode is the observation, x with the highest requency,. 1 N F For grouped data in a cumulative requency
More informationSTP 420 INTRODUCTION TO APPLIED STATISTICS NOTES
INTRODUCTION TO APPLIED STATISTICS NOTES PART - DATA CHAPTER LOOKING AT DATA - DISTRIBUTIONS Individuals objects described by a set of data (people, animals, things) - all the data for one individual make
More informationDepartment of Mathematics
Department of Mathematics TIME: 3 Hours Setter: DS DATE: 03 August 2015 GRADE 12 PRELIM EXAMINATION MATHEMATICS: PAPER II Total marks: 150 Moderator: AM Name of student: PLEASE READ THE FOLLOWING INSTRUCTIONS
More informationREVIEW: Midterm Exam. Spring 2012
REVIEW: Midterm Exam Spring 2012 Introduction Important Definitions: - Data - Statistics - A Population - A census - A sample Types of Data Parameter (Describing a characteristic of the Population) Statistic
More informationSampling, Frequency Distributions, and Graphs (12.1)
1 Sampling, Frequency Distributions, and Graphs (1.1) Design: Plan how to obtain the data. What are typical Statistical Methods? Collect the data, which is then subjected to statistical analysis, which
More informationSolutions with relevant marking scheme to Board Question papers available in downloadable PDF format at
15 Model Question Papers 12 Board Question Papers Salient Features Comprises a total of 27 Test Papers: (15 Model Question Papers + 12 Board Question Papers) Provides Model Question Papers with solutions
More informationMEASURES OF LOCATION AND SPREAD
MEASURES OF LOCATION AND SPREAD Frequency distributions and other methods of data summarization and presentation explained in the previous lectures provide a fairly detailed description of the data and
More informationMEASURES OF CENTRAL TENDENCY
INTRODUCTION: MEASURES OF CENTRAL TENDENCY Often, one encounters e term Measures of central tendency in a book on statistics (or an examination). One may also find mention of e term in a description of
More informationEnd of Year Examination Paper 2
End of Year Examination Paper 2 Instruction to andidates: Marks Obtained 1. Answer all questions. 2. Write your answers and working in the spaces provided. 3. Omission of essential working will result
More informationAlgebra I. Mathematics Curriculum Framework. Revised 2004 Amended 2006
Algebra I Mathematics Curriculum Framework Revised 2004 Amended 2006 Course Title: Algebra I Course/Unit Credit: 1 Course Number: Teacher Licensure: Secondary Mathematics Grades: 9-12 Algebra I These are
More informationWhat is Statistics? Statistics is the science of understanding data and of making decisions in the face of variability and uncertainty.
What is Statistics? Statistics is the science of understanding data and of making decisions in the face of variability and uncertainty. Statistics is a field of study concerned with the data collection,
More informationBBA - I YEAR DJB1C : BUSINESS MATHEMATICS AND STATISTICS SYLLABUS
BBA - I YEAR DJBC : BUSINESS MATHEMATICS AND STATISTICS SYLLABUS UNIT I: Measures of centraltendency Mean, Median, Mode, G.M. and H.M. Dispersion Range Q.D. M.D. S.D. C.V. UNIT II: Simple Correlation and
More informationDr. G.R. Damodaran college of Science Coimbatore GRD School of Commerce and International Business II B Com(CS) ( ) Semester IV
Dr. G.R. Damodaran college of Science Coimbatore 641 014 GRD School of Commerce and International Business II B Com(CS) (2016-2019) Semester IV Allied : Business Statistics - 405D Multiple Choice Question
More informationSTAT 200 Chapter 1 Looking at Data - Distributions
STAT 200 Chapter 1 Looking at Data - Distributions What is Statistics? Statistics is a science that involves the design of studies, data collection, summarizing and analyzing the data, interpreting the
More informationMeasures of Central Tendency
Statistics It is the science of assembling, analyzing, characterizing, and interpreting the collection of data. The general characterized of data: 1. Data shows a tendency to concentrate at certain values:
More informationChapter 1:Descriptive statistics
Slide 1.1 Chapter 1:Descriptive statistics Descriptive statistics summarises a mass of information. We may use graphical and/or numerical methods Examples of the former are the bar chart and XY chart,
More informationKeystone Exams: Algebra
KeystoneExams:Algebra TheKeystoneGlossaryincludestermsanddefinitionsassociatedwiththeKeystoneAssessmentAnchorsand Eligible Content. The terms and definitions included in the glossary are intended to assist
More informationLast Lecture. Distinguish Populations from Samples. Knowing different Sampling Techniques. Distinguish Parameters from Statistics
Last Lecture Distinguish Populations from Samples Importance of identifying a population and well chosen sample Knowing different Sampling Techniques Distinguish Parameters from Statistics Knowing different
More informationThis exam is closed book and closed notes. (You will have access to a copy of the Table of Common Distributions given in the back of the text.
TEST #3 STA 5326 December 4, 214 Name: Please read the following directions. DO NOT TURN THE PAGE UNTIL INSTRUCTED TO DO SO Directions This exam is closed book and closed notes. (You will have access to
More informationAll the men living in Turkey can be a population. The average height of these men can be a population parameter
CHAPTER 1: WHY STUDY STATISTICS? Why Study Statistics? Population is a large (or in nite) set of elements that are in the interest of a research question. A parameter is a speci c characteristic of a population
More informationProbabilities and Statistics Probabilities and Statistics Probabilities and Statistics
- Lecture 8 Olariu E. Florentin April, 2018 Table of contents 1 Introduction Vocabulary 2 Descriptive Variables Graphical representations Measures of the Central Tendency The Mean The Median The Mode Comparing
More informationProbability and Probability Distributions. Dr. Mohammed Alahmed
Probability and Probability Distributions 1 Probability and Probability Distributions Usually we want to do more with data than just describing them! We might want to test certain specific inferences about
More informationGlossary for the Triola Statistics Series
Glossary for the Triola Statistics Series Absolute deviation The measure of variation equal to the sum of the deviations of each value from the mean, divided by the number of values Acceptance sampling
More informationChapter 1: Revie of Calculus and Probability
Chapter 1: Revie of Calculus and Probability Refer to Text Book: Operations Research: Applications and Algorithms By Wayne L. Winston,Ch. 12 Operations Research: An Introduction By Hamdi Taha, Ch. 12 OR441-Dr.Khalid
More informationMgtOp 215 Chapter 3 Dr. Ahn
MgtOp 215 Chapter 3 Dr. Ahn Measures of central tendency (center, location): measures the middle point of a distribution or data; these include mean and median. Measures of dispersion (variability, spread):
More informationMathematical Fundamentals (Part 1)
Mathematical Fundamentals (Part 1) Mathematics Chapter 1 ALGEBRAIC OPERATIONS (+)(+) = POSITIVE (-)(-) = POSITIVE (+)(-) = NEGATIVE (-)(+) = NEGATIVE a x b a x (-b) = ab = -ab a(b + c) = ab + ac a(b -
More informationMicro Syllabus for Statistics (B.Sc. CSIT) program
Micro Syllabus for Statistics (B.Sc. CSIT) program Tribhuvan University Institute of Science & Technology(IOST) Level: B.Sc. Course Title: Statistics I Full Marks: 60 + 0 + 0 Course Code: STA 64 Pass Marks:
More informationLecture 1: Descriptive Statistics
Lecture 1: Descriptive Statistics MSU-STT-351-Sum 15 (P. Vellaisamy: MSU-STT-351-Sum 15) Probability & Statistics for Engineers 1 / 56 Contents 1 Introduction 2 Branches of Statistics Descriptive Statistics
More informationInstrumentation (cont.) Statistics vs. Parameters. Descriptive Statistics. Types of Numerical Data
Norm-Referenced vs. Criterion- Referenced Instruments Instrumentation (cont.) October 1, 2007 Note: Measurement Plan Due Next Week All derived scores give meaning to individual scores by comparing them
More informationMath 218 Supplemental Instruction Spring 2008 Final Review Part A
Spring 2008 Final Review Part A SI leaders: Mario Panak, Jackie Hu, Christina Tasooji Chapters 3, 4, and 5 Topics Covered: General probability (probability laws, conditional, joint probabilities, independence)
More informationVariables, distributions, and samples (cont.) Phil 12: Logic and Decision Making Fall 2010 UC San Diego 10/18/2010
Variables, distributions, and samples (cont.) Phil 12: Logic and Decision Making Fall 2010 UC San Diego 10/18/2010 Review Recording observations - Must extract that which is to be analyzed: coding systems,
More informationDepartment of Mathematics
Department of Mathematics TIME: 3 Hours Setter: DS DATE: 09 August 2016 GRADE 12 PRELIM EXAMINATION MATHEMATICS: PAPER II Total marks: 150 Moderator: GP Name of student: PLEASE READ THE FOLLOWING INSTRUCTIONS
More informationChapter # classifications of unlikely, likely, or very likely to describe possible buying of a product?
A. Attribute data B. Numerical data C. Quantitative data D. Sample data E. Qualitative data F. Statistic G. Parameter Chapter #1 Match the following descriptions with the best term or classification given
More informationSets and Set notation. Algebra 2 Unit 8 Notes
Sets and Set notation Section 11-2 Probability Experimental Probability experimental probability of an event: Theoretical Probability number of time the event occurs P(event) = number of trials Sample
More informationMeasures of center. The mean The mean of a distribution is the arithmetic average of the observations:
Measures of center The mean The mean of a distribution is the arithmetic average of the observations: x = x 1 + + x n n n = 1 x i n i=1 The median The median is the midpoint of a distribution: the number
More informationCurriculum Map for Mathematics SL (DP1)
Unit Title (Time frame) Topic 1 Algebra (8 teaching hours or 2 weeks) Curriculum Map for Mathematics SL (DP1) Standards IB Objectives Knowledge/Content Skills Assessments Key resources Aero_Std_1: Make
More informationThe science of learning from data.
STATISTICS (PART 1) The science of learning from data. Numerical facts Collection of methods for planning experiments, obtaining data and organizing, analyzing, interpreting and drawing the conclusions
More informationCollege Mathematics
Wisconsin Indianhead Technical College 10804107 College Mathematics Course Outcome Summary Course Information Description Instructional Level Total Credits 3.00 Total Hours 48.00 This course is designed
More informationYou are permitted to use your own calculator where it has been stamped as approved by the University.
ECONOMICS TRIPOS Part I Friday 11 June 004 9 1 Paper 3 Quantitative Methods in Economics This exam comprises four sections. Sections A and B are on Mathematics; Sections C and D are on Statistics. You
More informationMeasures of Central Tendency:
Measures of Central Tendency: Mean, Median, Mode CasperWendy Measures of Central Tendency Measure of central tendency provides a very convenient way of describing a set of scores with a single number that
More informationUnit 2 Maths Methods (CAS) Exam
Name: Teacher: Unit Maths Methods (CAS) Exam 1 014 Monday November 17 (9.00-10.45am) Reading time: 15 Minutes Writing time: 90 Minutes Instruction to candidates: Students are permitted to bring into the
More informationUNIVERSITY OF MASSACHUSETTS Department of Biostatistics and Epidemiology BioEpi 540W - Introduction to Biostatistics Fall 2004
UNIVERSITY OF MASSACHUSETTS Department of Biostatistics and Epidemiology BioEpi 50W - Introduction to Biostatistics Fall 00 Exercises with Solutions Topic Summarizing Data Due: Monday September 7, 00 READINGS.
More informationMarquette University MATH 1700 Class 5 Copyright 2017 by D.B. Rowe
Class 5 Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science Copyright 2017 by D.B. Rowe 1 Agenda: Recap Chapter 3.2-3.3 Lecture Chapter 4.1-4.2 Review Chapter 1 3.1 (Exam
More informationSummarizing Measured Data
Summarizing Measured Data 12-1 Overview Basic Probability and Statistics Concepts: CDF, PDF, PMF, Mean, Variance, CoV, Normal Distribution Summarizing Data by a Single Number: Mean, Median, and Mode, Arithmetic,
More informationDescriptive Statistics
Contents 36 Descriptive Statistics 36.1 Describing Data 2 36.2 Exploring Data 26 Learning outcomes In the first Section of this Workbook you will learn how to describe data sets and represent them numerically
More informationSUMMARIZING MEASURED DATA. Gaia Maselli
SUMMARIZING MEASURED DATA Gaia Maselli maselli@di.uniroma1.it Computer Network Performance 2 Overview Basic concepts Summarizing measured data Summarizing data by a single number Summarizing variability
More informationChapter Fifteen. Frequency Distribution, Cross-Tabulation, and Hypothesis Testing
Chapter Fifteen Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Copyright 2010 Pearson Education, Inc. publishing as Prentice Hall 15-1 Internet Usage Data Table 15.1 Respondent Sex Familiarity
More informationNote: Solve these papers by yourself This VU Group is not responsible for any solved content. Paper 1. Question No: 3 ( Marks: 1 ) - Please choose one
Paper Composed & Solved STA30 Finalterm Papers 7 Papers Solved.. By Arman Makhani Statistic and Probability STA30 7Final term paper Question No: ( Marks: ) - Please choose one Mean deviation is always:
More informationQUANTITATIVE DATA. UNIVARIATE DATA data for one variable
QUANTITATIVE DATA Recall that quantitative (numeric) data values are numbers where data take numerical values for which it is sensible to find averages, such as height, hourly pay, and pulse rates. UNIVARIATE
More informationADMS2320.com. We Make Stats Easy. Chapter 4. ADMS2320.com Tutorials Past Tests. Tutorial Length 1 Hour 45 Minutes
We Make Stats Easy. Chapter 4 Tutorial Length 1 Hour 45 Minutes Tutorials Past Tests Chapter 4 Page 1 Chapter 4 Note The following topics will be covered in this chapter: Measures of central location Measures
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 3HR Centre Number Tuesday 6 January 015 Afternoon Time: hours Candidate Number Higher Tier Paper Reference
More information104 Business Research Methods - MCQs
104 Business Research Methods - MCQs 1) Process of obtaining a numerical description of the extent to which a person or object possesses some characteristics a) Measurement b) Scaling c) Questionnaire
More informationMEASURES OF CENTRAL TENDENCY
MAT001-Statistics for Engineers MEASURES OF CENTRAL TENDENCY DESCRIPTIVE STATISTICAL MEASURES Graphical representation summarizes information in the data. In addition to the diagrammatic and graphic representations
More information