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S1 Coding Using coding to make numbers easier to work with when data values are large

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Mean and Standard Deviation Calculate the mean and standard deviation of the following data set 3,10,15,7,8 Add 3 to each of the numbers and recalculate the mean and standard deviation Subtract 2 from each of the numbers and recalculate the mean and standard deviation Multiply each of the numbers by 10 and recalculate the mean and standard deviation Divide each of the numbers by 2 and recalculate the mean and standard deviation

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Solutions What do you notice about the coded results compared to the original results? Why does this happen?

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Example 1 A data set has been coded using y= x / 10. The standard deviation is 1.41 Find the standard deviation of the original data. 1.41 x 10 = 14.1

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Example 2 A data set has been coded using y=x-20. The standard deviation is 3.641 Find the standard deviation of the original data. 3.641 as the standard deviation does not change

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Example 3 A data set has been coded using y=x+100. 2 The standard deviation is 12.342 Find the standard deviation of the original data. 24.684 Adding 100 has no effect but the division by 2 has halved the standard deviation

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E.G. 4 Time taken to complete reading a paper Time take (secs) Freq (f) Mid- point (x) Coding Y=x-500 1000 fyfy ² 0-300041500144 3000-6000164500464256 6000-8000870006.552338 8000-130002105001020200 Σf=30Σfy=140Σ fy ² =798 σ ² =798 – 140 ² = 4.82 30 30 Coded σ =2.19596 Original σ =2195.96

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