Question

(3.2.7) 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?
42,40,38,30,20,16,13,10,9.6,8.3

Answer 1

The mean is: $\bar{x}=\frac{42+40+38+30+20+16+13+10+9.6+8.3}{10}=22.69$.

The variance is:$\sigma^2=\frac{1}{10}((42-10)^2+(40-10)^2+(38-10)^2+(30-10)^2+(20-10)^2+(16-10)^2+(13-10)^2+(9.6-10)^2+(8.3-10)^2)=325.605$

The range is the difference between the smallest and the highest value. I.e.,

$r=42-8.3=33.7$

To make a good estimate we must know the total number of personalities and its mean. Most likely, it will be lower, if the number of personalities is big enough and their salaries are low with respect to the highest salaries.

Answer: 22.69; 325.605; 33.7