Coding (AQA A-Level Mathematics): Quizzes

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What is the primary purpose of coding in statistics?

To simplify calculations with data

What is the formula for coding a data value xx?

y=x−aby = \frac{x - a}{b}

In the coding formula y=x−aby = \frac{x - a}{b}, what does the constant aa do?

Shifts the data

What does the constant bb do in the coding formula?

Scales the data

If yˉ\bar{y} is the coded mean, what is the formula for the original mean xˉ\bar{x}?

xˉ=byˉ+a\bar{x} = b\bar{y} + a

How is the variance of the original data related to the coded variance?

Var(x)=b2×Var(y)\text{Var}(x) = b^2 \times \text{Var}(y)

How is the standard deviation of original data found from coded standard deviation?

SD(x)=b×SD(y)\text{SD}(x) = b \times \text{SD}(y)

What does coding NOT change in a data set?

Shape of the distribution

If yˉ=2\bar{y} = 2, a=50a = 50, and b=5b = 5, what is xˉ\bar{x}?

60

If Var(y)=3\text{Var}(y) = 3 and b=4b = 4, what is Var(x)\text{Var}(x)?

48

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