of the squares of the differences from the mean Ism 9 C Chapter 5 Review: Statistics

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1 Distribution, ZScore, Confidence 2 Key Concepts: Central Tendency, Standard Deviation, Graphing, Normal C a Ism ZScore Table p.592 Practice Questions p.240, p Summary: p , p Textbook p Chapter 5 Review: Statistics 9 C 7 d) Standard Deviation c) Mode b)median 1 cc a) Mean (( 1 t If I 5? 6,4,9,4,8,5 Example: Find all measures of central tendency for the following list of numbers: number of values of the squares of the differences from the mean FORMULA FOR STANDARD DEVIATION: the C.y\ 3) Mode = The number that occurs Wi 4 (4e vi 4) Standard Deviation = The average Cb sfc of each number from numbers in the list) 2) Median = The W LCC 9t.x._ number (might be halfway between two how many there are. 1) Mean = The calculated Add up the numbers and divide by Central Tendency

2 5 L2. Examples: Histogram = Frequency Polygon = L11 L. 1 3 S crd Step#1:$(AT. 6it. Normal Distribution Step #2: STA7. C 1C. I St# category. For large data like this, you can input the numbers into your calculator to find the Sccr Test Score measures of central tendency. Remember to use the Wid(.L number for each P1LO c ( S x ia_ II 28 L 13 3t 85 4 r,_ r I 1 I I / I \ 1 \ /\ tendency. We also drew graphs to represent the data: For larger sets of data, we break it into chunks to find the measures of central Graphing O

3 c C Formula: z = 0 7 vo [Ci i/ Cvt. i7 C4tc cfb2i C12 Lj 5ccr Ce b) Find the percentage of people who score a C (between 60% and 73%) LI 3 c ( /,.7j 2 a) Label the normal curve standard deviation of 7%. Key Example: The average score on an normally distributed exam is 64% with a estimate from the survey. (example: this survey is correct 19 times out of 20) 3) Confidence level = the probability that the answer in reallife matches your of ±3%) survey and reallife. (example: 40% will vote Conservative with a margin of error 2) Margin of error = the possible difference between your estimate based on the people are likely to vote for the Liberal party) using information obtained from a sample. (example: between 9.5 and 10.2 million 1) Confidence interval = a specific interval estimate of the whole population by For interpreting a survey Confidence 6 If 1 am 0.6 standard deviations below the mean, then my zscore isic If! am 1.5 standard deviations above the mean, then my zscore isj The zscore is the distance from a point to the fri. in terms of ZScores

4 a) Mode(s) 12 quizzes: 14,12,17,3,8,12,15,8,10,11 Practice #1: Find the measures of central tendency for the marks on sample of 10 b) Median M C 7 S d) Standard Deviation 6x /cs c) Mean x:? 2 a) Mode(s) t S,? S /f&f L\) Score (out of 100) a) L3 7<; 0 $5 5 U C >, Geography Test Scores 1 tz Practice #3: Find the measure of central tendency for the following histogram: 1qc 7 ( s 3 b. In which year are the heights most consistent?, L, S c3 r71t /999. y: I7 3 if a. Determine the mean and standard deviation for each year. 2011: : kindergarten in 1999 and again when they graduated from high school in Practice #2: Students recorded their heights, in inches, when they graduated from d) Standard Deviation 3 j f2t3/2_,7i c) Mean IIC b) Median 3 IL) I I 12 ), 0 2 C) Chapter 5 Review: Statistics

5 I 2)/ L H± ic i(c / 1 // C / Groüp J 118J ( LJ E JU i3c takes the test will score between 90 and 110? mean of 100 and a standard deviation of 10, what is the probability that a person who Practice #5: Suppose scores on an IQ test are normally distributed. If the test has a 5)1O ff44.t J1 3) / LiQ I9 i+fi. H41 *[ 1)100 jfi HIf Interval Frequency b) Construct a histogram of the data. a) Make a frequency table with five intervals to organize the pulse rates. Groups j lj Groüp f GroupI Practice #4: Four groups of students recorded their pulse rates after a 2 km run. r J/ 1//i. v

6 can be allowed. milliliters ofsoda, find the greatest standard deviation, to the nearest hundredth, that GOci/ / s_ / (1 J 3 the probability of getting less than 80 on the test? Practice #10: An IQ test has a mean of 100 with a standard deviation of 15. What is b) Less than 0.55?, a)lessthan 1.61? o9 t 3 Practice #9: What is the probability of getting a zscore of... C1qr oqi C/4AT 5,VLE? t=120,a=10,x=125 /ZcZj (2, Determine the percent of data to the left of the zscore: z = Determine the percent of data to the right of the zscore: z = C c Practice #7: Determine the zscore for the given value. Practice #8: ( C) sç c normally distributed, if at least 99.7% of the bottles must have between 585 and 595 each bottle varies slightly. Suppose the amount ofsoda dispensed into the bottles is Practice #6: A machine is used to fill soda bottles. The amount ofsoda dispensed into

7 / e) Who will win the election? has a mean of 520 km and a standard deviation of 14 km. What percent of the time does Yumi drive between 508 km and 538 km on a tank of gas? depending on the weather and the amount she drives on the highway. The distance error 7 for Smith and 47% would vote for Jones. The results were stated as being accurate within 3.8 percentage points, 19 times out of 20. size, but used a confidence level of 99%, what would happen to the margin of were held today, whom would you vote for? The results indicated that 53% would vote C/1,zrr iif 1 qo, She keeps track of the distance she drives on each tank of gas. The distance varies d) If the polling company conducted this same survey using the same sample C4 Smith, and how many will vote for Jones? Practice #11: Yumi always waits until her gas tank is nearly empty before refuelling. Practice #13: A poll was conducted to ask voters the following question: If an election c) What is the confidence level? 1 Ict(o c?0.) ( 31i /q7l? b) If the number of people likely to vote is , how many people will vote for a) What is the confidence interval (percentage)? 5, : f Eç; f?.2 5.C 7/ ill 37) /

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