1. GCSE Statistics
More on Averages

2. 4.5 Transforming Data GCSE Statistics only
Sometimes it is easier to calculate the mean by transforming the data
I have seen this referred to as using an assumed mean (yr. 9 impact maths book?)
Here’s some data find the mean
Find the difference using an assumed mean of 70
Find the mean of these numbers = 11
Add this to your assumed mean = this is the mean of the original data

3. Same data different assumed mean 
Here’s some data find the mean
Find the difference using an assumed mean of 80
Find the mean of these numbers = −4+1− = = 1
Add this to your assumed mean = this is still the mean of the original data

4. Measure Advantages Disadvantages
4.6 Deciding which average to use
Measure
Advantages
Disadvantages
MODE
Use when the data are non numeric or when asked to find the most popular item
Easy to find
Can be used with any type of data
Unaffected by open-ended or extreme values
The mode will be a data value
Mathematical properties are not useful
There is not always a mode or sometimes there is more than one
MEDIAN
Use the median to describe the middle of a set of data that has an extreme value
Easy to calculate
Unaffected by extreme values
MEAN
Use the mean to describe the middle of a set of data that does not have an extreme value
Uses all the data
Mathematical properties are well known and useful
Always affected by extreme values
Can be distorted by open ended classes
Page 130 stats book page 40 unit 1

5. Which average would you use for these sets of data?
Red, red, blue, green, blue yellow
£10, £10, £10, £15, £15, £15, £20, £20, £22
Wage (£)
frequency
600 5
800 20
1000
100
1200 8
2500 2
6000 1

6. In each of the following questions, explain why you would use the MODE, MEDIAN or MEAN average
The GCSE results for a group C C C C D D D B D C C C
The wages of 10 people working in an office £150 £180 £190 £330 £120 £240 £450 £500 £125 £270
The average height of a group of people
The average amount of money spent by a Year 9 student during the weekend
5) The average number of days in a month

7. 4.7 Weighted Mean GCSE Statistics only
When you sit an exam one paper can hold more importance than another and the results are weighted
The papers for your GCSE maths are weighted
Unit 1 is 30% of the final mark
Unit 2 is 30% of the final mark
Unit 3 is 40% of the final mark
Your final result will be worked out using this weighting.

8. 4.7 Weighted Mean GCSE Statistics only
Example

9. Example

10. Example

11. 4.8 Measures of Spread These are also known as measures of dispersion.
You have met the range = largest value – smallest value
You have may have met quartiles before in the context of cumulative frequency graphs
and their best buddy the interquartile range
New to you may be percentiles and deciles
variance (we will look at this after unit 1 is finished)
standard deviation (we will look at this after unit 1 is finished)

12. The Range
A crude measure of spread as it only takes into account the largest and smallest of the data values
Example 1
find the range of:
Range = 24 – 6 = 18

13. The Range
Example 2
The speeds v, (to the nearest mile per hour), of cars on a motorway were recorded by the police.
estimate the range of the speeds
Speed v (mph)
Frequency
20 < v ≤ 30 2
30 < v ≤ 40 14
40 < v ≤ 50 29
50 < v ≤ 60 22
60 < v ≤ 70 13
the speeds are given to the nearest mph
lowest speed = 20.5 mph
highest speed = 70.5 mph
range = 70.5 – 20.5 = 50 mph

14. The Quartiles (Bob and Frank)
the lower quartile Q1 is the value such that one quarter (25%) of the values are less than or equal to it
the middle quartile Q2 is the median
the upper quartile Q3 is the value such that three quarters (75%) of the values are less than or equal to it
the median and quartiles split the data into four equal parts. That is why they are called quartiles!
A frequently used measure of spread is the inter-quartile range
inter-quartile range (IQR) = upper quartile – lower quartile (Q3 – Q1)
page 135 has the formulae for finding the quartiles

15. Example
Put the data in order
find out how many data items you have
n = 7
Q1 = ¼(7 + 1 ) = 2nd value which is 5
Q3 = ¾(7 + 1) = 6th value which is 12
inter-quartile range = Q3 - Q1
= 12 – 5
= 7

16. Turn to the book page 135 to look at finding quartiles in frequency tables

17. Turn to the book page 139 to find out about percentiles and deciles
there is no way I can get that graph on this screen until I buy the revision guide!

18. GCSE Statistics
Exercise 4D page 129 – assumed mean
Exercise 4E page choosing your average
Exercise 4F page Weighted mean
Exercise 4G page 139 – Measures of Spread
GCSE Maths Unit 1
Exercise 2E page 41 – Using the three types of average
Exercise 2J page 51 – range and interquartile range