Problem

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?
\[
\begin{array}{lllllllllll}
40 & 39 & 38 & 32 & 20 & 16 & 14 & 10 & 9.8 & 9.2 & \text { 문 }
\end{array}
\]
The range of the sample data is $\$ 30.8$ million. (Type an integer or a decimal.)
The variance of the sample data is (Round to two decimal places as needed.)

Answer

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Answer

Calculating the standard deviation, we get \(12.342122994039558\). So, the standard deviation of the sample data is \(\boxed{12.34}\).

Steps

Step 1 :Given the top 10 annual salaries (in millions of dollars) of TV personalities are: 40, 39, 38, 32, 20, 16, 14, 10, 9.8, 9.2.

Step 2 :The range of a set of data is the difference between the highest and lowest values in the set. To find the range, we subtract the smallest data value from the largest data value in the data set.

Step 3 :Calculating the range, we get \(40 - 9.2 = 30.8\). So, the range of the sample data is \(\boxed{30.8}\) million.

Step 4 :The variance of a set of data is a measure of how much values in the dataset vary on average from the mean of the data. To calculate the variance, we first find the mean of the data. Then for each number in the dataset, we subtract the mean and square the result. The variance is the average of these squared differences.

Step 5 :Calculating the variance, we get \(152.328\). So, the variance of the sample data is \(\boxed{152.33}\).

Step 6 :The standard deviation is the square root of the variance. It is a measure of the amount of variation or dispersion of a set of values.

Step 7 :Calculating the standard deviation, we get \(12.342122994039558\). So, the standard deviation of the sample data is \(\boxed{12.34}\).

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