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! Wednesday, 26 April 2017

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

Calculating the mean from a frequency table The following frequency table shows the scores obtained when a dice is thrown 50 times. What is the mean score? Score Frequency 1 2 3 4 5 6 8 11 9 7 Total 50 Score × Frequency 8 22 18 36 45 42 171 Explain that to find the mean score we need to find the total score altogether. A 1 was scored 8 times and so we can find the score obtained by throwing 1s by multiplying 8 × 1. A 2 was scored 11 times and so we can find the score obtained by throwing 2s by finding 11 × 2. Conclude that we need to find the score × the frequency for each score. Show how this can be done by revealing the yellow row in the table. We can then record the total number of throws and the total score in the blue column. The mean is found by dividing these totals. 171 50 The mean score = = 3.42

Complete Questions: Page 84 Exercise 8.3 1-4 Remember: Mean = Sum of values Number of values 3 + 6 + 7 + 9 + 9 5 34 5 = = 6.8

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: 2, 1, 0, 3, 1. 2, 1, 0, 3, 1. The modal score is 2. Is it possible to have more than one modal value? Yes Is it possible to have no modal value? Yes

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. Method of travel Frequency Bicycle 6 On foot 8 Car 2 Bus Train 3 What is the modal method of travel? 8 Most children travel on foot. Stress that the modal method will have the highest frequency. Travelling on foot is therefore the modal method of travel.

Finding the mode from a bar chart This bar chart shows the scores in a science test: 1 2 3 4 5 6 7 8 9 10 Number of pupils Marks out of ten This bar chart can be edited by double clicking on it in Normal view. What was the modal score? 6 is the modal score because it has the highest bar.

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? Ask pupils to tell you how many people were surveyed (200). Ask pupils to tell you what percentage of people liked each type of food. The biggest sector of the pie chart is for chocolate, so this is the modal food type.

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

Complete Questions Page 85 Exercise 8.4 Questions1-6 MODE MEANS MOST

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, 8, 6, Write the values in order: 6, 7, 7, 8, 9, 10, 12. The median is the middle value.

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 Pupils may wish to use other mental methods to find a number half-way between two others, such as imagining the numbers on a number line, particularly if the numbers are close together. ½ of 4 = 2 2 + 47 = 49 The median of 42, 43, 47, 51, 56 and 65 is 49.

Class Work Page 87 Exercise 8.5 1-4 Remember: Write the values in order: 6, 7, 7, 8, 9, 10, 12. The median is the middle value.

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 small it tells us that the values are similar in size. What does it mean if the range is small? When the range is large it tells us that the values vary widely in size. What does it mean if the range is large?

Class Work Page 88 Exercise 8.7 1-8 Remember: Range = highest value – lowest value 1,2,3,8,9,4,5,7 ------------Range=9-1=8

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

Remember the three averages and range L A R G E S T M M E D I A N M I D D L E M O D E C O M N M E A N A D D I V I D E

The three averages and range There are three different types of average: MEAN sum of values number of values MEDIAN middle value MODE most common The range is not an average, but tells you how the data is spread out: RANGE largest value – smallest value