The following relative frequency distribution was constructed from a population
ID: 3441633 • Letter: T
Question
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
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.)
Explanation / Answer
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]