24.4 Averages from frequency tables — Learn

Prerequisites: multiplication, division and the mean of a list.

Objectives: calculate the mean, median, mode and range from a frequency table where the data values are given.

A frequency table records each value and how many times it occurs. To find the mean, multiply each value by its frequency, add those products, then divide by the total frequency.

Example. The values 1, 2 and 3 have frequencies 2, 3 and 1. Find the mean and median.

Multiply values by frequencies: $1\times2=2$, $2\times3=6$, $3\times1=3$.

Add products: $2+6+3=11$.

Add frequencies: $2+3+1=6$.

Mean $=11/6$.

The cumulative frequencies are 2, 5 and 6.

The middle positions are 3 and 4. Both lie among the first five values, which are 1, 1, 2, 2, 2.

So the middle pair is 2 and 2, and the median is $2$.

Mode $=2$ because its frequency is greatest. Range $=3-1=2$.

Watch out. Do not divide the weighted total by the number of rows. Divide by the total frequency.

Progress check

The travel survey can be recorded as categories and frequencies. What would the total frequency count, and why?

You should now be able to

• calculate a mean using value times frequency;
• find the median by using cumulative counts in a frequency table;
• identify the mode and range from the values and frequencies.