EXAMPLE 2.9.9

A number of people invested $1000 each in the Gomer Family of Mutual Funds. The frequency table below shows the current values of those investments. Compute the mean, median and mode.

 

VALUEFREQUENCY
Value 0Frequency 48
Value 50Frequency 42
Value 75Frequency 31
Value 100Frequency 28
Value 150Frequency 22

EXAMPLE 2.9.9 SOLUTION

First find n, the total number of people involved.

n = 48 + 42 + 31 + 28 + 22 = 171

 

Now find the mode.

mode = $0 because 0 is the value with the highest frequency.

 

Next we find the mean:

mean = [(48 times 0) plus (42 times 50) plus (31 times 75) plus (28 times 100) plus (22 times 150) ] divided by 171
= 10,525 divided by 171
= $61.55

 

Finally we find the median. In order to do so, we first find the position of the "middle of the list."

(n plus 1) divided by 2
= 172 divided by 2
= 86.
To find the median, we must count frequencies until we have found the eighty-sixth number
The first 48 numbers are all zeroes. The next 42 numbers are all fifties. This means that the forty-ninth through ninety-eighth numbers are all fifties, so in particular the eighty-sixth number is a fifty.

The median is $50.