This document provides information and examples about calculating various averages (mean, median, mode) and the range from sets of data. It defines each average type and explains how to calculate the mean from a frequency table. Examples are given to find the mean, median, mode and range for sets of test scores and daily temperatures. It also shows how to calculate the mean from a frequency table listing the number of houses with different numbers of children.

1. Handling data 2 BTEOTSSSBAT: Calculate the mean, mode, median and range of a set of data Find the mean from a frequency table

2. Key words Mean Median Mode Range Frequency

3. Mean, median and mode There are three types of average: mean, mode and median. Mode This is the one that occurs the most. Median This is the one in the middle, when all the numbers have been put into numerical order. Mean This is the one that we normally think of when we are asked to find the average. Mean = Total of the scores No of scores

4. Range The range is also an important piece of information. It tells us how spread out the information is. Range = largest – smallest

5. Example Here are the scores that 5 people get for a test. 6 7 5 6 6 Find (a) the mean (b) the mode and (c) the median score and (d) the range (a) Mean = 6 + 7 + 5 + 6 + 6 = 30 5 5 = 6 (b) Mode: 6 occurs the most (3 times) so the mode is 6 (c) Median Step 1: put in numerical order: 5, 6, 6, 6, 7 Step 2: identify the middle number: 5, 6, 6, 6, 7 So the median is 6. (d) The range is 7 – 5 = 2.

6. Now try these 1 Five other people take the same test and their scores are: 5 3 5 5 7 Find (a) the mean (b) the mode (c) the median score and (d) the range The following are the midday temperatures over a week: 23 C 24C 25C 26C 20C 23C 27C Find (a) the mean (b) the mode (c) the median score and (d) the range

7. Using frequency tables If we survey 120 houses and asked how many people under the age of 16 lived in the house, we might get the following results: Range = 6-0 = 6 Highest frequency = mode Mode = 0

8. 37  0 = 0 23  1 = 23 1.51 children The mean number of children per house would then be

9. Now try these 2 1 .The number of children per family on a housing estate were recorded as follows: Find (a) the range (b) the mode and (c) the mean number of children per family.

10. 2. An agricultural researcher counted the number of peas in a pod in a certain strain as follows: Find (a) the range (b) the mode and (c) the mean number of children per family.