1. Handling Data: AVERAGES Learning Objective: To be able to calculate the mode, median, range and Mean KEY WORDS: MEDIAN, MODE, RANGE, MEAN and AVERAGES All MUST be able understand how to calculate mode, median, range and Mean Some should be able to know which average is the best to USE!

2. The mean The mean is the most commonly used average. It can only be used with numerical data. To calculate the mean of a set of values we add together the values and divide by the total number of values. Mean = Sum of values Number of values For example, the mean of 3, 6, 7, 9 and 9 is 3 + 6 + 7 + 9 + 9 5 = 34 5 = 6.8

3. Finding the mode The mode or modal value in a set of data is the data value that appears the most often. For example, the number of goals scored by the local football team in the last ten games is: The modal score is 2. Is it possible to have more than one modal value? Is it possible to have no modal value? Yes 2,1,2,0, 2,3,1,2,1.2,2,1,2,2,0, 2,2,3,1,2,2,1.

4. Finding the mode The mode is the only average that can be used for categorical or non-numerical data. For example, 30 pupils are asked how they usually travel to school. The results are shown in a frequency table. What is the modal method of travel? Method of travelFrequency Bicycle6 On foot8 Car2 Bus6 Train3 8 Most children travel on foot. Travelling on foot is therefore the modal method of travel.

5. Finding the mode from a bar chart This bar chart shows the scores in a science test: What was the modal score? 6 is the modal score because it has the highest bar.

6. Finding the mode from a pie chart This pie chart shows the favourite food of a sample of people: What was the modal food type? The biggest sector of the pie chart is for chocolate, so this is the modal food type.

7. Finding the mode from a frequency table This frequency table shows the frequency of different length words in a given paragraph of text. What was the modal word length? For this data there are two modal word lengths: 2 and 4. We need to look for the word lengths that occur most frequently. Word length Frequency 1 3 2 16 3 12 4 16 5 7 6 3 7 11 8 6 9 2 10 1 16

8. Finding the median The median is the middle value of a set of numbers arranged in order. For example, Find the median of 10,7,9,12,7,8,6, Write the values in order: 6,7, 8,9,10,12. The median is the middle value.

9. Finding the median To find the number that is half-way between 47 and 51 we can add the two numbers together and divide by 2. 47 + 51 2 = 98 2 = 49 Alternatively, find the difference between 47 and 51 and add half this difference to the lower number. 51 – 47 = 4 ½ of 4 = 2 2 + 47 = 49 The median of 42, 43, 47, 51, 56 and 65 is 49.

10. What does it mean if the range is large? What does it mean if the range is small? Finding the range The range of a set of data is a measure of how the data is spread across the distribution. To find the range we subtract the lowest value in the set from the highest value. Range = highest value – lowest value When the range is large it tells us that the values vary widely in size. When the range is small it tells us that the values are similar in size.

11. Plenary Come up with ONE WORD TO describe the 3 AVERAGES and RANGE Mode: Median: Mean: Range:

12. Remember the three averages and range M O D E COOMMONCOOMMONO M E A N A AADDAADD D I V I D E M E D I A N DMIDDLEDMIDDLE R A N G E LAARGESTLAARGESTA SMALLEESTSMALLEESTE

13. The three averages and range There are three different types of average: M ODE most common M EAN sum of values number of values M EDIAN middle value The range is not an average, but tells you how the data is spread out: R ANGE largest value – smallest value