Linear Coding


Linear coding is used for:
• simplifying messy arithmetic.
• converting between different units.

An example would be:



This table gives the height (we'll call this column h of different people. We can simplify this table by making up a rule to help us. We could replace the h values by x values, which could be the main difference in height between them - found by subtracting the lowest height - 170 - from the other values in the h column.



We could then simplify x further by dividing the values in the x column by 2.



Sometimes you're asked to work out the mean and standard deviation from a table that's been simplified like that one. All you need to do is undo the workings that's already been done to get the raw data and work from that. Either that or you are given the mean, standard deviation and variance that's been worked out using the coded data and you need to find the mean and standard deviation of the original data. In this example, we can make a formula for the coded data:

x = h - 170 ⁄ 2
Mean of h = 2(mean of x) + 170
= 2(Σxf ⁄ Σf) + 170
= 2(0 + 2 + 6 + 3 + 16 ⁄ 17) + 170
= 2(27 ⁄ 17) + 170
= 2(1.5882352941176470588235294117647) + 170
= 173.2cm (1 decimal place)



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