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2 variable univariate data measure of central tendency parameter statistic margin of sampling error measure of variation variance standard deviation

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4 Measures of Central Tendency A. SALARIES A new Internet company has 3 employees who are paid $300,000, 10 who are paid $100,000, and 60 who are paid $50,000. Which measure of central tendency best represents the pay at this company? Since most of the employees are paid $50,000, the higher values are outliers. Answer: Thus, the median or mode best represents the available jobs.

5 A. In a cereal contest, there is 1 Grand Prize of $1,000,000, 10 first prizes of $100, and 50 second prizes of $10. Which measure of central tendency best represents the prizes? A. mean B. median C. mean or median D. median or mode A. A B. B C. C D. D

6 Measures of Central Tendency B. Which measure of central tendency best represents the following data, and why? 37, 33, 40, 31, 33, 38, 35 Answer: The mean is the best measure of central tendency, since there are no outliers.

7 B. Which measure of central tendency best represents the following data, and why? 87, 93, 90, 91, 93, 40, 82 A. The mean, since ther are no outliers. B. The median, since there is one outlier. C. The mode, since there are repeated numbers. A B A. A B. B C. C 0% 0% 0% C

8 Samples Versus Populations A. Determine whether the following represents a population or a sample. A company has each of its employees complete a survey on commuting habits. Answer: This represents a population because the survey is completed by every employee.

9 A. Determine whether the following represents a population or a sample. Every 4th student is stopped to complete a survey on the theme for a school dance. A. This represents a population. B. This represents a sample. A. A B. B 0% 0% A B

10 Samples Versus Populations B. Determine whether the following represents a population or a sample. Every 5th table in the cafeteria is interviewed to find out what students eat for lunch. Answer: This represents a sample because only a fraction of students were interviewed.

11 B. Determine whether the following represents a population or a sample. The baseball team is asked about the color of their new uniforms. A. This represents a population. B. This represents a sample. A. A B. B 0% 0% A B

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13 Margin of Sampling Error A. In a random survey of 1710 teens, 76% said they had downloaded music from the internet. What is the margin of sampling error? Margin of sampling error Margin of Sampling Error Formula n = Simplify. Answer: The margin of sampling error is about ±2.42%.

14 Margin of Sampling Error B. In a random survey of 1710 teens, 76% said they had downloaded music from the internet. What is the likely interval that contains the percentage of the population that have downloaded music from the internet? = = Answer: The likely interval that contains the percentage of the population that have downloaded music from the internet is between 73.58% and 78.42%.

15 A. In a random survey of 1540 people, 83% said they had rented a DVD from the store. What is the margin of sampling error? A. 1.96% B. 2.11% C. 2.31% D. 2.55% A B A. A B. B C. C 0% D. D 0% 0% 0% C D

16 B. In a random survey of 1540 people, 83% said they had rented a DVD from the store. What is the likely interval that contains the percentage of the population that have rented a DVD from the store? A. between 79.38% and 81.92% B. between 80.45% and 85.55% C. between 84.54% and 87.08% D. between 85.54% and 88.08% A B A. A B. B C. C 0% D. D 0% 0% 0% C D

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18 Standard Deviation A. WEATHER The daily high temperatures (in F) in a city for the first 10 days of last year were 38, 48, 51, 53, 64, 69, 51, 53, 43, and 36. For the first 10 days of this year, they were 32, 17, 30, 34, 35, 40, 43, 36, 38, and 28. Use a calculator to find the standard deviation of the first 10 days of this year s temperatures.

19 Standard Deviation Clear all lists. Then press STAT ENTER and enter each data value, pressing ENTER after each value. To view the statistics, press STAT 1 ENTER. The mean of the first 10 days of this year s temperatures is 33.3 with a standard deviation of about 6.9

20 A. Use a calculator to find the standard deviation of the population of data below. A B C D A. A B. B C. C 0% D. D 0% 0% 0% A B C D

21 Standard Deviation B. WEATHER The daily high temperatures (in F) in a city for the first 10 days of last year were 38, 48, 51, 53, 64, 69, 51, 53, 43, and 36. For the first 10 days of this year, they were 32, 17, 30, 34, 35, 40, 43, 36, 38, and 28. Compare the standard deviations for the two years. Answer: There was a greater variation in temperature for the first 10 days of last year.

22 B. Compare the standard deviations of the data sets in part A and part B. Which statement is true? A is greater than 4.16, so the data in part A are more spread out than the data in part B. B is greater than 4.16, so the data in part A are closer to the mean than the data in part B. A. A B. B

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DATA HANDLING (3) Overview. Measures of dispersion (or spread) about the mean (ungrouped data) Lesson. Learning Outcomes and Assessment Standards

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