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!
Wednesday, 26 April 2017

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 5 34 5 =
= 6.8

3. 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

4. Complete Questions: Page 84 Exercise 8.3 1-4 Remember: Mean =
Sum of values
Number of values 5 34 5 =
= 6.8

5. 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

6. 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.

7. 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.

8. 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.

9. 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.

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

11. 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.

12. 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. 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
= 49
The median of 42, 43, 47, 51, 56 and 65 is 49.

13. 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.

14. 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?

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

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

17. Remember the three averages and rangeL 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

18. 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