The following relative frequency distribution was constructe

The following relative frequency distribution was constructed from a population of 500. Calculate the population mean, the population variance, and the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Class    

Relative Frequency

  20 up to 10

0.34

  10 up to 0

0.22

  0 up to 10

0.30

  10 up to 20

0.14

  Population mean

  Population variance

  Population standard deviation

Solution

We get the midpoints of each class then treat those as the individual x values.

Consider the table:          
          
x   P(x)   x P(x)   x^2 P(x)
-15   0.34   -5.1   76.5
-5   0.22   -1.1   5.5
5   0.3   1.5   7.5
15   0.14   2.1   31.5
          
Totals       -2.6   121
       =E(x)   =E(x^2)
          
Thus,          
          
E(x) =    -2.6   [ANSWER, MEAN]  

Var(x) = E(x^2) - E(x)^2 =    114.24   [answer, variance]  

s(x) =    10.68831137 [answer, standard deviation]