Question

Consider the following graph.

Stem-and-leaf plot of ages of college professors with key stem 5 with leaf 3 means 53. The plot includes the following data: stem 3 with leaves 0 and 2; stem 4 with leaves 1, 4, 4, and 5; stem 5 with leaves 3, 5, 8, and 9; stem 6 with leaves 2, 2, 2, 5, 6, and 8; and stem 7 with leaves 5, 5, and 6.



Calculate the mean.



Explain what the mean would signify for the entire population of college professors by using this sample.

Answer 1

the average age for the entire population of college professors is 56 years old

Answer 2

The mean of the data set is 56.42.

The mean signify that the average age of college professors is about 56 years.

Explanation:

The given stem-and-leaf plot represents the ages of college professors.

From the given stem-and-leaf plot we get the data set

30,32, 41, 44, 44, 45, 53, 55, 58, 59, 62, 62, 62, 65, 66, 68, 75, 75, 76

The formula for mean is

`Mean=(\sum x)/(n)`

where, x are observations and n is sample size.

Using the formula, the mean of the given data set is

`Mean=(30+32+41+44+44+45+53+55+58+59+62+62+62+65+66+68+75+75+76)/(19)`

`Mean=(1072)/(19)`

`Mean\approx 56.42`

The mean of the data set is 56.42.

The mean signify that the average age of college professors is about 56 years.