1. Objective: Understand and use the MEAN value of a data set

2. 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

3. The mean
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

4. Problems involving the mean
A pupil scores 78%, 75% and 82% in three tests. What was the mean of the three test scores?
Encourage pupils to check the answer by adding 78, 75, 82 and 85 and dividing by four.

5. Problems involving the mean
The maximum temperature in Haslemere during one week was as follows:
6, 9, 10, 15, 4, 6, 7
What was the mean of the temperatures?
Encourage pupils to check the answer by adding 78, 75, 82 and 85 and dividing by four.

6. 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

7. Obj: Finding the mean
Impact Maths 1R
Page 327
Exercise 17A

8. Objective: Understand and use the Mode or modal value of a data set

9. 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

10. What was the modal score?
Finding the mode
A dice was thrown ten times. These are the results:
What was the modal score?
3 is the modal score because it appears most often.

11. Finding the mode The mode is the only average that can be used for
non-numerical data.
For example, 25 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?
Most children travel by foot.
Stress that the modal method will have the highest frequency.
Travelling on foot is therefore the modal method of travel.

12. Finding the mode from a bar chart
This bar chart shows the scores in a science test:
Number of pupils
This bar chart can be edited by double clicking on it in Normal view.
Mark out of ten
What was the modal score?
6 is the modal score because it has the highest bar.

13. 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.

14. Finding the modal class for continuous data
This grouped frequency table shows the times 50 girls and 50 boys took to complete one lap around a race track.
Frequency
Time (minutes:seconds)
Boys
Girls
2:00 ≤ 2:15 3 1
2:15 ≤ 2:30 7 6
2:30 ≤ 2:45 11 10
2:45 ≤ 3:00 13 9
3:15 ≤ 3:30 8 12
3:30 ≤ 3:45
3:45 ≤ 4:00 2
What is the modal class for the girls?
What is the modal class for the boys?
What is the modal class for the pupils regardless of whether they are a boy or a girl?
Establish that the modal class for the girls is 3:15  3:30 and modal class for the boys is 2:45  3:00.
To find the modal class for both boys and girls we must add the two frequencies in each row together. The modal class is 2:45  3:00.

15. 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

16. 1R chapter 17 B page 329
Q1a 5, 2, 8, 2, 6, 8, 4, 2, 6, 9
Put in ascending order
2, 2, 2, 4, 5, 6, 6, 8, 8, 9
Mode = 2

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. Mean height of 7W2

19. 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.

20. Finding the median
When there is an even number of values, there will be two values in the middle.
For example,
Find the median of 56, 42, 47, 51, 65 and 43.
In this case, we have to find the mean of the two middle values.
The values in order are:
42,
43,
47,
51,
56,
65.
There are two middle values, 47 and 51.

21. 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
The median of 42, 43, 47, 51, 56 and 65 is 49.
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.

22. The median

23. 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

24. 6, 2, 9, 1, 4, 8, 5, 9, 7 Impact Maths 1R Page 331 – Exercise 17C
Finding the Median
Impact Maths 1R
Page 331 – Exercise 17C
6, 2, 9, 1, 4, 8, 5, 9, 7

25. What is the rogue value in the following data set:
Rogue values
The median is often used when there is a rogue value – that is, a value that is much smaller or larger than the rest.
What is the rogue value in the following data set:
192, 183, 201, 177, 193, 197, 4, 186, 179?
The mean of this data set is:
The median of this data set is:
Point out that rogue values are not typical of the rest of the data. If we found the mean of data containing a rogue value then the mean would be unrepresentative of the data set.
4, 177, 179, 183, 186, 192, 193, 197, 201.
The median of the data set is not affected by the rogue value, 4.

26. Mean or median?
Would it be better to use the median or the mean to represent the following data sets?
34.2, , , 356, , ?
median
0.4, 0.5, 0.3, 0.8, 0.7, 1.0?
mean
892, 954, , 908, 871, 930?
mean
3.12, , , , , ?
median
Ask pupils to identify the rogue value, if there is one, and to use this to justify their choice of mean or median.
97.85, , , , , ?
mean
87634, , , , , ?
median

27. Objective: Understand and use the range of a data set

28. Understand the range of a data setL A R G E S T M
M E A N A D
D I V I D E

29. 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
2, 5, 3, 2, 8, 1, 6, 5,
1, 2, 2, 3, 5, 5, 6, 8
Range = 8 – 1 = 7

30. Key Words
Ascending
Numbers which are increasing in value
Descending
Numbers which are decreasing in value
Examples of Ascending and Descending
3, 4, 12, 25, 36, 42
ascending
42, 36, 25, 12, 4, 3
descending
Objective : To understand the terms used.

31. Objective : To place data in ascending or descending order.
Questions
Write these numbers in ascending order what is the range:
Range = 15 – 4 = 11
Write these numbers in descending order what is the range:
Range = 72 – 24 = 48

32. Finding the range
Impact Maths 1R
Page 332 – Exercise 17D
6, 8, 3, 9, 7, 2, 5, 5, 3
2, 3, 3, 5, 5, 6, 7, 8, 9
Range = = 7

33. 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. 1, 3, 5, 5, 6, 7 Range = 6
What does it mean if the range is small?
When the range is large it tells us that the values vary widely in size. 1, 6, 67, 83, 99 Range = 98
What does it mean if the range is large?

34. Have we achieved the objective: understanding and finding the Range
Write three sentences about your understanding of range

35. 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

36. The mean

37. Find the missing value
Pupils must use the information given to find the missing value.

38. 6, 8, 3, 9, 7, 2, 5, 5, 3 Finding the range Impact Maths 1R
Page 332 – Exercise 17D
6, 8, 3, 9, 7, 2, 5, 5, 3

39. 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 5 12 4 10 7 6 11 8 9 12
What was the modal word length?
1, 1, 1, 2, 2, 2, 2, 2, 3, ….
2 and 4 are the modal word lengths because they both appeared 16 times.

40. Finding the modal class for continuous data
This grouped frequency table shows the times 50 girls and 50 boys took to complete one lap around a race track.
Frequency
Time (minutes:seconds)
Boys
Girls
2:00 ≤ 2:15 3 1
2:15 ≤ 2:30 7 6
2:30 ≤ 2:45 11 10
2:45 ≤ 3:00 13 9
3:15 ≤ 3:30 8 12
3:30 ≤ 3:45
3:45 ≤ 4:00 2
What is the modal class for the girls?
What is the modal class for the boys?
What is the modal class for the pupils regardless of whether they are a boy or a girl?
Establish that the modal class for the girls is 3:15  3:30 and modal class for the boys is 2:45  3:00.
To find the modal class for both boys and girls we must add the two frequencies in each row together. The modal class is 2:45  3:00.

41. Finding the mode The mode is the only average that can be used for
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 by foot.
Stress that the modal method will have the highest frequency.
Travelling on foot is therefore the modal method of travel.

42. Finding the Modal Group
Impact Maths 2G
Page 236 – Exercise 15B
Impact Maths 2G
Page 243 – Exercise 15F

43. 1R chapter 17 B page 329
Q1a 5, 2, 8, 2, 6, 8, 4, 2, 6, 9
Put in ascending order
2, 2, 2, 4, 5, 6, 6, 8, 8, 9
Mode = 2

44. 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