Mean and Standard deviation Problems with Solutions

Mean and standard deviation problems are presented. Problems related to data sets as well as grouped data are discussed. The solutions to these problems are at the bottom of the page.

Consider the following three data sets A, B and C.

A = {9,10,11,7,13}

B = {10,10,10,10,10}
Find

C = {1,1,10,19,19}

a) Calculate the mean of each data set.

b) Calculate the standard deviation of each data set.

c) Which set has the largest standard deviation?

d) Is it possible to answer question c) without calculations of the standard deviation?

A given data set has a mean μ and a standard deviation σ.

a) What are the new values of the mean and the standard deviation if the same constant k is added to each data value in the given set?Explain.

b) What are the new values of the mean and the standard deviation if each data value of the set is multiplied by the same constant k?Explain.

If the standard deviation of a given data set is equal to zero, what can we say about the data values included in the given data set?

The frequency table of the monthly slaries of 20 people is shown below.

salary(in $)

frequency

3500

5

4000

8

4200

5

4300

2

a) Calculate the mean of the salaries of the 20 people.

b) Calculate the standard deviation of the salaries of the 20 people.

The following table shows the grouped data, in classes, for the heights of 50 people.

height (in cm) - classes

frequency

120 <- 130

2

130 <- 140

5

140 <- 150

25

150 <- 160

10

160 <- 170

8

a) Calculate the mean of the salaries of the 20 people.

b) Calculate the standard deviation of the salaries of the 20 people.