Find the range, variance, standard deviation for the sample data. Given that these are the top 10 salaries.

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 personaliites in general?

 

42, 40, 39, 33, 21, 19, 17, 16 15.5, 14.2

Answer 1

The set of 10 values={42, 40, 39, 33, 21, 19, 17, 16, 15.5, 14.2}

Range is the difference between the highest and the lowest values of the set =42-14.2=27.8

Mean={42+40+39+ 33+21+19+17+16 +15.5+14.2}/10=256.7/10=25.67

S.D=±√[{(25.67-42)²+(25.67-40)²+(25.67-39)²+(25.67-33)²+(25.67-21)²+(25.67-19)²+(25.67-17)²+(25.67-16)²+(25.67-15.5)²+(25.67-14)²}/(10-1)]

=±√[{266.6689+205.3489+177.6889+53.7289+21.8089+44.4889+75.1689+93.5089+103.4289+131.5609}/9]

=±√[1248.5699/9]

=±√[138.72998888888888888888888888889]

=±11.77836953440028934843269187781

Variance=±[{(25.67-42)²+(25.67-40)²+(25.67-39)²+(25.67-33)²+(25.67-21)²+(25.67-19)²+(25.67-17)²+(25.67-16)²+(25.67-15.5)²+(25.67-14)²}/(10-1)]
=±[{266.6689+205.3489+177.6889+53.7289+21.8089+44.4889+75.1689+93.5089+103.4289+131.5609}/9]
=±[1248.5699/9]

=±138.72998888888888888888888888889

 

Given that these are the top 10 salaries, we can only say that the minimum and maximum of the top 10 salaries varies widely. And also, in general, the salaries of TV personalities varies quite widely.