Question

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 37 36 30 20 18 17 16 15.8 14.3

Answer 1

first, we need to arrange the data in ascending order

14.3, 15.8, 16,17,18,20,30,36,37,39

Range = maximum value - minimum value = 39 - 14.3 = 24.7

For variance, we first need to find the value of the mean of the given 10 data points

we know that the mean = (sum of all the given data points)/(total number of the data points)

setting the given values, we get

mean = (14.3+15.8+16+17+18+20+30+36+37+39)/(10) = 243.1/10 = 24.31

Sample variance=

where and are the given data values

setting the values, we get

Sample variance=

And we know that standard deviation is square root of the variance

so, we can write it as

sample standard deviation=

No, we can't know anything about the variation of salaries of TV personalities in general based on the top 10 because the given data values represent only top 10, so the data insufficient for making any conclusion.