GCSE Statistics More on Averages. 4.5 Transforming Data GCSE Statistics only Sometimes it is easier...
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Transcript of GCSE Statistics More on Averages. 4.5 Transforming Data GCSE Statistics only Sometimes it is easier...
GCSE StatisticsMore on Averages
4.5 Transforming Data GCSE Statistics only
Sometimes it is easier to calculate the mean by transforming the dataI have seen this referred to as using an assumed mean (yr. 9 impact maths book?)
Here’s some data find the mean
76 81 73 92 83
Find the difference using an assumed mean of 70
6 11 3 22 13
Find the mean of these numbers = 11
Add this to your assumed mean 70 + 11 = 81 this is the mean of the original data
Same data different assumed mean
Here’s some data find the mean
76 81 73 92 83
Find the difference using an assumed mean of 80
-4 1 -7 12 3
Find the mean of these numbers = = 1
Add this to your assumed mean 80 + 1 = 81 this is still the mean of the original data
Measure Advantages Disadvantages
MODEUse 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
MEDIANUse the median to describe the middle of a set of data that has an extreme value
• Easy to calculate• Unaffected by extreme
values• Mathematical properties
are not useful
MEANUse 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
4.6 Deciding which average to use
Page 130 stats book page 40 unit 1
Which average would you use for these sets of data?
1. Red, red, blue, green, blue yellow2. £10, £10, £10, £15, £15, £15, £20, £20, £223.
Wage (£) frequency
600 5
800 20
1000 100
1200 8
2500 2
6000 1
In each of the following questions, explain why you would use the MODE, MEDIAN or MEAN average
1) The GCSE results for a group C C C C D D D B D C C C
2) The wages of 10 people working in an office £150 £180 £190 £330 £120 £240 £450 £500 £125 £270
3) The average height of a group of people
4) The average amount of money spent by a Year 9 student during the weekend
5) The average number of days in a month
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 markUnit 2 is 30% of the final markUnit 3 is 40% of the final mark
Your final result will be worked out using this weighting.
4.7 Weighted Mean GCSE Statistics only
Example
Example
Example
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 graphsand 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)
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: 12 6 18 24
Range = 24 – 6 = 18
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 mphlowest speed = 20.5 mphhighest speed = 70.5 mph
range = 70.5 – 20.5 = 50 mph
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
Example
7 9 13 5 6 12 3
Put the data in order
3 5 6 7 9 12 13
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
Turn to the book page 135 to look at finding quartiles in frequency tables
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!
GCSE Statistics
Exercise 4D page 129 – assumed meanExercise 4E page 131 - choosing your averageExercise 4F page 133 - Weighted meanExercise 4G page 139 – Measures of Spread
GCSE Maths Unit 1
Exercise 2E page 41 – Using the three types of averageExercise 2J page 51 – range and interquartile range