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Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general? 40 38 37 30 18 14 12 9. 8.9 8.3 D

Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general? 40 38 37 30 18 14 12 9. 8.9 8.3 D

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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### Understanding Measures of Statistical Dispersion #### Sample Data Analysis - **Range of the sample data:** $32.0 million (Type an integer or a decimal.) - **Variance of the sample data:** 163.66 (Round to two decimal places as needed.) - **Standard deviation of the sample data:** $12.79 million (Round to two decimal places as needed.) #### Question on Standard Deviation: **Question:** Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in general? **Answer Choices:** - A. Yes, because the sample is random. - B. Yes, because the standard deviation is an unbiased estimator. - C. No, because the sample is not representative of the whole population. (Correct Answer) - D. No, because there is an outlier in the sample data. --- ### Explanation: This example illustrates the calculation and interpretation of basic statistical measures of dispersion—range, variance, and standard deviation. The sample data suggests that the range is $32.0 million, the variance is 163.66, and the standard deviation is $12.79 million. The range provides a basic measure of spread by looking at the difference between the highest and lowest values in the dataset. The variance and standard deviation offer more sophisticated tools, rootly reflecting the average degree to which each number is different from the mean. Among the provided choices, the selected answer (C) indicates a potential issue with the representativeness of the sample, a common concern when using sample data to make generalizations about a population.
Transcribed Image Text:### Understanding Measures of Statistical Dispersion #### Sample Data Analysis - **Range of the sample data:** $32.0 million (Type an integer or a decimal.) - **Variance of the sample data:** 163.66 (Round to two decimal places as needed.) - **Standard deviation of the sample data:** $12.79 million (Round to two decimal places as needed.) #### Question on Standard Deviation: **Question:** Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in general? **Answer Choices:** - A. Yes, because the sample is random. - B. Yes, because the standard deviation is an unbiased estimator. - C. No, because the sample is not representative of the whole population. (Correct Answer) - D. No, because there is an outlier in the sample data. --- ### Explanation: This example illustrates the calculation and interpretation of basic statistical measures of dispersion—range, variance, and standard deviation. The sample data suggests that the range is $32.0 million, the variance is 163.66, and the standard deviation is $12.79 million. The range provides a basic measure of spread by looking at the difference between the highest and lowest values in the dataset. The variance and standard deviation offer more sophisticated tools, rootly reflecting the average degree to which each number is different from the mean. Among the provided choices, the selected answer (C) indicates a potential issue with the representativeness of the sample, a common concern when using sample data to make generalizations about a population.
### Top 10 Annual Salaries of TV Personalities Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities: 40, 38, 37, 30, 18, 14, 12, 9, 8.9, 8.3 **Analytical Task:** - Find the range, variance, and standard deviation for the sample data. - Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general? **Steps to Follow:** 1. **Range:** - Definition: The range is the difference between the highest and the lowest values in a data set. - Calculation: Range = Maximum value - Minimum value 2. **Variance:** - Definition: Variance measures how far a set of numbers are spread out from their average value. - Calculation: Variance is calculated by taking the average of the squared differences from the mean. 3. **Standard Deviation:** - Definition: The standard deviation is a measure of the amount of variation or dispersion in a set of values. - Calculation: Standard Deviation is the square root of the variance. By analyzing the range, variance, and standard deviation, you can infer the variation and spread of salaries among TV personalities.
Transcribed Image Text:### Top 10 Annual Salaries of TV Personalities Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities: 40, 38, 37, 30, 18, 14, 12, 9, 8.9, 8.3 **Analytical Task:** - Find the range, variance, and standard deviation for the sample data. - Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general? **Steps to Follow:** 1. **Range:** - Definition: The range is the difference between the highest and the lowest values in a data set. - Calculation: Range = Maximum value - Minimum value 2. **Variance:** - Definition: Variance measures how far a set of numbers are spread out from their average value. - Calculation: Variance is calculated by taking the average of the squared differences from the mean. 3. **Standard Deviation:** - Definition: The standard deviation is a measure of the amount of variation or dispersion in a set of values. - Calculation: Standard Deviation is the square root of the variance. By analyzing the range, variance, and standard deviation, you can infer the variation and spread of salaries among TV personalities.
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