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Objective:
Understand and use the MEAN value of a data set
Remember the three averages and range
M O D EM O D ECOOMMON
M E A NM E A NAADDD I V I D E
M E D I A NM E D I A N
MIDDDLE
R A N G ER A N G ELAARGEST
SMALLEEST
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
3 + 6 + 7 + 9 + 9
5=
34
5= 6.8
Problems involving the mean
A pupil scores 78%, 75% and 82% in three tests. What was the mean of the three test scores?
%3.783
%235
3
%82%75%78
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?
Co1.87
57
7
764151096
Remember the three averages and range
M O D EM O D ECOOMMON
M E A NM E A NAADDD I V I D E
M E D I A NM E D I A N
MIDDDLE
R A N G ER A N G ELAARGEST
SMALLEEST
Obj: Finding the mean
Impact Maths 1R
Page 327
Exercise 17A
Objective:
Understand and use the Mode or modal value of a
data set
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
Yes
2, 1, 2, 0, 0, 2, 3, 1, 2, 1.2, 1, 2, 0, 0, 2, 3, 1, 2, 1.
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.
Finding the mode
The mode is the only average that can be used fornon-numerical data.
For example, 25 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 travel
Frequency
Bicycle 6
On foot 8
Car 2
Bus 6
Train 3
Most children travel by foot.
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:
What was the modal score?
6 is the modal score because it has the highest bar.
0
1
2
3
4
5
6
7
8
9
1 2 3 4 5 6 7 8 9 10
Mark out of ten
Nu
mb
er o
f p
up
ils
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
116 16
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 7 10
3:45 ≤ 4:00 1 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?
Remember the three averages and range
M O D EM O D ECOOMMON
M E A NM E A NAADDD I V I D E
M E D I A NM E D I A N
MIDDDLE
R A N G ER A N G ELAARGEST
SMALLEEST
1R chapter 17 B page 329
Q1a 5, 2, 8, 2, 6, 8, 4, 2, 6, 9
2, 2, 2, 4, 5, 6, 6, 8, 8, 9
Mode = 2
Put in ascending order
Remember the three averages and range
M O D EM O D ECOOMMON
M E A NM E A NAADDD I V I D E
M E D I A NM E D I A N
MIDDDLE
R A N G ER A N G ELAARGEST
SMALLEEST
Mean height of 7W2
Height
Mean = Total 0 = 0No of pupils 1
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, 7, 8, 9, 10, 12.
The median is the middle value.
Finding the median
When there is an even number of values, there will be two values in the middle.
In this case, we have to find the mean of the two middle values.
For example,
Find the median of 56, 42, 47, 51, 65 and 43.
The values in order are:
There are two middle values, 47 and 51.
42, 43, 47, 51, 56, 65.
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
The median of 42, 43, 47, 51, 56 and 65 is 49.
The median
Remember the three averages and range
M O D EM O D ECOOMMON
M E A NM E A NAADDD I V I D E
M E D I A NM E D I A N
MIDDDLE
R A N G ER A N G ELAARGEST
SMALLEEST
Finding the Median
Impact Maths 1R
Page 331 – Exercise 17C
6, 2, 9, 1, 4, 8, 5, 9, 7
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 median of this data set is:
4, 177, 179, 183, 186, 192, 193, 197, 201.
The median of the data set is not affected by the rogue value, 4.
The mean of this data set is:
1689
1791864197193177201183192
Mean or median?
Would it be better to use the median or the mean to represent the following data sets?
34.2, 36.8, 29.7, 356, 42.5, 37.1?
0.4, 0.5, 0.3, 0.8, 0.7, 1.0?
892, 954, 1026, 908, 871, 930?
3.12, 3.15, 3.23, 9.34, 3.16, 3.20?
97.85, 95.43, 102.45, 98.02, 97.92, 99.38?
87634, 9321, 78265, 83493, 91574, 90046?
median
mean
mean
median
mean
median
Objective:
Understand and use the range of a data set
Understand the range of a data set
M E A NM E A NAADDD I V I D E
R A N G ER A N G ELAARGEST
SMALLEEST
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
Key Words
Ascending
Descending
Numbers which are increasing in value
Numbers which are decreasing in value
Examples of Ascending and Descending
3, 4, 12, 25, 36, 42
42, 36, 25, 12, 4, 3
ascending
descending
Objective : To understand the terms used.
Questions
Write these numbers in ascending order what is the range:
12 4 15 6 5 10
Write these numbers in descending order what is the range:
45 54 24 56 72 67
Objective : To place data in ascending or descending order.
4 5 6 10 1215
72 67 56 54 45 24
Range = 15 – 4 = 11
Range = 72 – 24 = 48
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 = 9 - 2 = 7
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. 1, 6, 67, 83, 99 Range = 98
When the range is small it tells us that the values are similar in size. 1, 3, 5, 5, 6, 7 Range = 6
Have we achieved the objective:
understanding and finding the Range
Write three sentences about your understanding of range
Remember the three averages and range
M O D EM O D ECOOMMON
M E A NM E A NAADDD I V I D E
M E D I A NM E D I A N
MIDDDLE
R A N G ER A N G ELAARGEST
SMALLEEST
The mean
Find the missing value
Finding the range
Impact Maths 1R
Page 332 – Exercise 17D
6, 8, 3, 9, 7, 2, 5, 5, 3
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?
Word length
Frequency
1
3
2
5
3
12
4
10
5
7
6
3
7
11
8
6
9
2
10
112
1, 1, 1, 2, 2, 2, 2, 2, 3, ….
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 7 10
3:45 ≤ 4:00 1 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?
Finding the mode
The mode is the only average that can be used fornon-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 travel
Frequency
Bicycle 6
On foot 8
Car 2
Bus 6
Train 3
8Most children travel by foot.
Travelling on foot is therefore the modal method of travel.
Finding the Modal Group
Impact Maths 2G
Page 236 – Exercise 15B
Impact Maths 2G
Page 243 – Exercise 15F
