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Data Coding (Edexcel AS Maths): Revision Note

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Coding

Sometimes data needs to be coded for further use with calculations. This is particularly useful with data that deals with very small or very large numbers, or with data that needs to be classified for research purposes.

What is coding?

  • Coding is a way of simplifying data to make it easier to work with

  • The coding must be carried out on all values within the data set and will normally be done using a given formula

  • Coding can be carried out in a number of ways:

    • Adding or subtracting a constant to each data value

    • Multiplying or dividing each data value by a constant

    • A combination of both of the above

How are statistical calculations carried out with coded data?

  • If you know the mean or standard deviation of the original data it is possible to find the mean or standard deviation of the coded data and vice versa

  • It is important to remember what the mean and standard deviation actually tell us about the data to understand how coding calculations work

    • The mean is a measure of location, changing the data set in any way will cause the mean to change in the same way

    • The standard deviation is a measure of spread, adding or subtracting a constant to every value within the data set will not change the standard deviation of the data set

      • Multiplying or dividing every value within the data set by a constant will change the standard deviation by the modulus of the constant

      • If the data were coded by multiplying or dividing by a negative, the standard deviation will change by the equivalent positive value

  • Anytime calculations are carried out on data that has been coded,

    • The original mean can be found by solving the equation to reverse the coding

    • For example, if the data, begin mathsize 16px style x end style, was coded using the formula

y equals a x plus b

Then the mean of the coded data, begin mathsize 16px style y with bar on top end style would be   

y with bar on top equals a x with bar on top plus b

The original mean, begin mathsize 16px style x with bar on top end style , will be  begin mathsize 16px style x with bar on top space equals fraction numerator y with bar on top space minus b over denominator a end fraction end style

  • The original standard deviation

    • Will be the same as the coded standard deviation if the data was coded by adding or subtracting a constant only

    • Can be found by reversing the coding if the data was coded by multiplying or dividing by a constant only

    • If the data was coded by a combination of both then only the multiplying or dividing will need to be reversed to find the original standard deviation

    • For example, if the data, was coded using the formula

y space equals space a x plus b

Then the standard deviation of the coded data, begin mathsize 16px style sigma subscript y end stylewould be

sigma subscript y equals open vertical bar a close vertical bar sigma subscript x

The original standard deviation, begin mathsize 16px style sigma subscript x end style, will be

sigma subscript x equals fraction numerator sigma subscript y over denominator open vertical bar a close vertical bar end fraction

Worked Example

The shoulder height, h comma of a group of Asian elephants living in a nature reserve are summarised in the table below.

Height, cm

Frequency, bold italic f

 200 space less or equal than space h space less than space 220

2

 220 space less or equal than space h space less than space 240

5

 240 space less or equal than space h space less than space 260

8

 260 space less or equal than space h space less than space 280

8

 280 space less or equal than space h space less than space 300

5

 300 space less or equal than space h space less than space 320

2

(i) Code the data using the formula x space equals space fraction numerator h minus 250 over denominator 20 end fraction

 

(ii) Use the coded data to find an estimate for the mean and standard deviation, you may use the summary statistics straight capital sigma x f space equals space 15 comma space straight capital sigma x squared f space equals space 59 comma space straight capital sigma space f equals 30.

2-1-4-coding-we-solution-part-1
2-1-4-coding-we-solution-part-2

Examiner Tips and Tricks

  • Be careful when using the formulae for the mean and standard deviation with coded summary statistics, you must make sure that you use the summary statistics consistently throughout. For example, if you use the sum of the coded data squared in the formula for the standard deviation, you must subtract the square of the coded mean.

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    Amber

    Author: Amber

    Expertise: Maths

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.