Statistics: Mean, Median & Mode – JSS1 Mathematics Lesson Note (Third Term)

An average is a single value used to represent a set of numbers. The mean is the sum of the values divided by the number of values. The median is the middle value after the data is arranged in order. The mode is the value that occurs most often.

Behavioural objectives

By the end of the lesson, students should be able to:

1. explain what an average is;
2. calculate the mean of a set of data;
3. find the median of a set of data, including when there are two middle values;
4. identify the mode, including when there are two modes (bimodal);
5. prepare a frequency table from raw data and draw a bar chart from it.

What is an average?

An average is a single value used to represent a set of numbers (that is, all the values in a set of data). The average is the most commonly used statistic.

How do you find the mean, median and mode?

• Mean = sum of the values ÷ number of values
• Median = the number in the middle after the data is arranged in increasing or decreasing order
• Mode = the value that occurs most frequently

Worked example

Calculate the mean, median and mode of the following data.

1. 45, 50, 55, 54, 48, 53, 50, 55
2. 38, 35, 36, 30.8, 34.7, 37.9, 33.1
3. 3, 0, 4, 7, 0, 5, 3, 4, 0, 3, 6, 5, 5, 4, 6, 5

Solution for the first set of data:

Mean

Mean = (∑x) ÷ n, that is, the addition of all the given items divided by the number of items.

Mean = (45 + 50 + 55 + 54 + 48 + 53 + 50 + 55) ÷ 8

= 410 ÷ 8

= 51.25

Median

Arrange the data in order: 45, 48, 50, 50, 53, 54, 55, 55.

There are eight values, so there are two middle values, 50 and 53. The median is their mean.

Median = (50 + 53) ÷ 2 = 103 ÷ 2 = 51.5

Mode

The data is bimodal. The modes are 50 and 55.

How do you prepare a frequency table and bar chart?

The figures below show the number of children per family in a sample of 40 houses in a street.

1, 2, 4, 3, 5, 3, 8, 3, 2, 2, 3, 4, 5, 6
5, 4, 2, 1, 3, 2, 4, 5, 3, 8, 7, 6, 5, 4
5, 7, 6, 3, 8, 6, 3, 5, 7, 5, 4, 3

Prepare a frequency table to represent the information. Then draw a bar chart to represent the information.

Bar chart showing the number of children per family in a sample of 40 houses

The vertical axis shows the frequency, from 0 to 10. The horizontal axis shows the number of children per family, from 1 to 8.

Evaluation

1. What is an average?
2. State how to find the mean, the median and the mode of a set of data.
3. How do you find the median when there are two middle values?
4. Calculate the mean, median and mode of the second and third sets of data in the worked example.

Assignment

Do these exercises:

• Exercise 24.1, page 263, numbers 2, 4, 5 and 6
• Exercise 24.3, page 266, numbers 3 and 4