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

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Presentation transcript:

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

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

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

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 x 10 = 14.1

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

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

E.G. 4 Time taken to complete reading a paper Time take (secs) Freq (f) Mid- point (x) Coding Y=x fyfy ² Σf=30Σfy=140Σ fy ² =798 σ ² =798 – 140 ² = Coded σ = Original σ =