Question

Question 5 The following table gives the frequency distribution of the amounts of telephone bills for August 2012 for a sample of 50 families. Amount of Telephone Bill (dollars) 40 to less than 70 70 to less than 100 100 to less than 130 130 to less than 160 160 to less than 190 Number of Families 12 10 16 Calculate the mean, variance, and standard deviation Round your answers to two decimal places. Mean Variance Standard deviation-$

Answer 1

The classes for amount of bill and the number of families are given

Class "40 to less than 70" means 40 - 70 and number of families are nothing but the frequencies

Mean:

The formula to find mean is

fr Mean

Where f - frequency of class and x - mid point of class

The formula to find the midpoints x is,

The midpoint of first class 40 - 70 is

40+70

Similarly the midpoints of the remaining classes are 85, 115, 145 and 175 respectively.

Therefore, Mean = $128.8

Variance:

The formula to find the variance is,

Therefore, variance is 1587.31

Standard deviation:

Standard deviation is the square root of variance

Standard deviation-VVariance = 1587.31-39.84

Therefore, the standard deviation is $39.84