Coding (Edexcel A-Level Mathematics): Quizzes

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Coding
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What is the primary purpose of coding in statistics?

To simplify calculations with large numbers

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

The original data value

What is the role of constant aa in the coding formula?

To shift the data

What is the role of constant bb in the coding formula?

To scale the data

How does coding affect the shape of the data distribution?

It doesn't change the shape

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

xˉ=byˉ+a\bar{x} = b\bar{y} + a

What formula converts the original mean xˉ\bar{x} to the coded mean yˉ\bar{y}?

yˉ=xˉ−ab\bar{y} = \frac{\bar{x} - a}{b}

How do you find original variance from coded variance?

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

How do you find original SD from coded SD?

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

Which constant affects the variance and standard deviation in coding?

Only bb

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

60

When is coding especially useful?

With large numbers or awkward decimals

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