GCSEStatistics: HigherEdexcelRevision NotesProcessing, Representing & Analysing DataMeasures of Central TendencyTransforming Data

Transforming Data (Edexcel GCSE Statistics)

Revision Note

Roger

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Roger

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Maths

Transforming Data

What effect does transforming data have on the mean, median and mode?

  • If all the data values in a data set are increased (or decreased) by the same amount

    • then the mean, mode and median will each also increase (or decrease) by the same amount

      • e.g. if the original mean is 14

      • and 20 is added to each data value

      • then the new mean will be 20+14 = 34

  • If all the data values in a data set are multiplied (or divided) by the same number

    • then the mean, mode and median will each also be multiplied (or divided) by the same number

      • e.g. if the original median is 19

      • and all the data values are multiplied by 2

      • then the new median will be 19x2 = 38

    • This includes increasing or decreasing all the data values by the same percentage

      • e.g. increasing all the values by 10%, by multiplying them all by 1.1

      • or decreasing all the values by 10%, by multiplying them all by 0.9

Why is transforming data useful?

  • If you already know the mean, mode and/or median for a data set

    • then you can find those averages quickly for a transformed data set

      • i.e. without having to recalculate them all from scratch

  • Transforming data can also make it easier to calculate averages in the first place

    • i.e. by giving you 'nicer' numbers to work with

    • e.g. for the values 1001.2, 1000.8, 1002.4, 1003.8, 1002.4

      • Subtract 1000 from each value: 1.2, 0.8, 2.4, 3.8, 2.4

      • Multiply each of those values by 10: 12, 8, 24, 38, 24

      • For those transformed numbers, Mean=21.2, Mode=24, Median=24

    • To find the averages for the original data values, undo the transformations in reverse order

      • Divide each average by 10: Mean=2.12, Mode=2.4, Median=2.4

      • Add 1000 to each of those: Mean=1002.12, Mode=1002.4, Median=1002.4

Exam Tip

  • An exam question won't always tell you to transform data before calculating averages

    • If the question doesn't tell you to, then you don't have to

    • But remembering it as a useful 'trick' that can

      • save you time

      • make calculation errors less likely

Worked Example

A chicken farmer takes a sample of 10 eggs from his chickens, in order to determine an average weight for the eggs that his hens lay. The weights of the eggs in the sample (in grams) are:

63.2      67.4      69.1      67.9      64.3      68.5      66.2      63.8      65.0      66.7


(a) Work out the mean and median weights for the farmer's sample, by first transforming the data to make it easier to use.

This data can be made simpler by subtracting 60 from all the values

3.2      7.4      9.1      7.9      4.3      8.5      6.2      3.8      5.0      6.7

Find the mean of the transformed values by adding them together and dividing by the total number of values (10)

fraction numerator 3.2 plus 7.4 plus 9.1 plus 7.9 plus 4.3 plus 8.5 plus 6.2 plus 3.8 plus 5.0 plus 6.7 over denominator 10 end fraction equals 6.21

To find the mean of the original values, undo the transformation by adding 60

mean equals 6.21 plus 60 equals 66.21

To find the median of the transformed values first write them in order

3.2      3.8      4.3      5.0      6.2      6.7      7.4      7.9      8.5      9.1

Cross off from the ends to find the middle values

3.2       3.8       4.3       5.0      6.2      6.7      7.4      7.9      8.5      9.1

The median is halfway between 6.2 and 6.7

fraction numerator 6.2 plus 6.7 over denominator 2 end fraction equals 6.45

To find the median of the original values, undo the transformation by adding 60

median equals 6.45 plus 60 equals 66.45

Don't forget to include units in your final answer!

mean = 66.21 g
median = 66.45 g

The farmer is considering using a new chicken feed that says it will increase the weight of eggs laid by 3%.

(b) If the claim about the new feed is true, estimate what the mean and median weights of the farmer's hens' eggs will be if he starts using the new feed. Give your answers correct to 2 decimal places.

If the weight of all the hens' eggs increase by 3%, then the mean and median weights will also increase by 3%

To increase the averages found in part (a) by 3%, multiply them by 1.03
3% increase means we want 3% on top of the original 100%
(103% as a decimal multiplier is 1.03)

new space mean equals 66.21 cross times 1.03 equals 68.1963 new space median equals 66.45 cross times 1.03 equals 68.4435

Round your answers to 2 d.p.

new mean = 68.20 g (2 d.p.)
new median = 68.44 g (2 d.p.)

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    Roger

    Author: Roger

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.