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? 39 38 37 30 20 18 17 16 15.8 14.5 O The range of the sample data is Smillion. (Type an integer or a decimal.) The variance of the sample data is|. (Round to two decimal places as needed.) The standard deviation of the sample data is S million. (Round to two decimal places as needed.) Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in general? O A. No, because the sample is not representative of the whole population. O B. Yes, because the standard deviation is an unbiased estimator. O C. No, because there is an outlier in the sample data. O D. Yes, because the sample is random.

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### Sample Data Analysis on TV Personalities' Salaries

Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. We aim to calculate the range, variance, and standard deviation for this sample data. With this information, we can speculate on the variation of salaries for TV personalities in general. The salaries are:

39, 38, 37, 30, 20, 18, 17, 16, 15.8, 14.5

1. **Range of the Sample Data:**
   - The range is the difference between the highest and lowest value within the data set.

2. **Variance of the Sample Data:**
   - Variance measures how far each number in the data set is from the mean and thus from every other number in the set.

3. **Standard Deviation of the Sample Data:**
   - The standard deviation is a measure of the amount of variation or dispersion in a set of values.

We are tasked with filling in the following:
- The range of the sample data is \$_____ million.
- The variance of the sample data is _____ (round to two decimal places).
- The standard deviation of the sample data is \$_____ million (round to two decimal places).

#### Evaluating the Sample's Representation:

**Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in general?**

- **Option A: No, because the sample is not representative of the whole population.**
- **Option B: Yes, because the standard deviation is an unbiased estimator.**
- **Option C: No, because there is an outlier in the sample data.**
- **Option D: Yes, because the sample is random.**

Each option provides a perspective on whether the calculated standard deviation appropriately reflects the general variation in salaries.

### Summary:

This exercise teaches important statistical concepts such as range, variance, and standard deviation, and encourages critical thinking about data representation and analysis.
Transcribed Image Text:### Sample Data Analysis on TV Personalities' Salaries Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. We aim to calculate the range, variance, and standard deviation for this sample data. With this information, we can speculate on the variation of salaries for TV personalities in general. The salaries are: 39, 38, 37, 30, 20, 18, 17, 16, 15.8, 14.5 1. **Range of the Sample Data:** - The range is the difference between the highest and lowest value within the data set. 2. **Variance of the Sample Data:** - Variance measures how far each number in the data set is from the mean and thus from every other number in the set. 3. **Standard Deviation of the Sample Data:** - The standard deviation is a measure of the amount of variation or dispersion in a set of values. We are tasked with filling in the following: - The range of the sample data is \$_____ million. - The variance of the sample data is _____ (round to two decimal places). - The standard deviation of the sample data is \$_____ million (round to two decimal places). #### Evaluating the Sample's Representation: **Is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in general?** - **Option A: No, because the sample is not representative of the whole population.** - **Option B: Yes, because the standard deviation is an unbiased estimator.** - **Option C: No, because there is an outlier in the sample data.** - **Option D: Yes, because the sample is random.** Each option provides a perspective on whether the calculated standard deviation appropriately reflects the general variation in salaries. ### Summary: This exercise teaches important statistical concepts such as range, variance, and standard deviation, and encourages critical thinking about data representation and analysis.
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