Easy -1.2 This is a straightforward application of the standard formulas for how linear transformations affect mean and standard deviation. Students only need to recall that mean transforms as μ_y = 1.4μ_x - 20 and SD transforms as σ_y = 1.4σ_x, then solve two simple linear equations. No problem-solving or conceptual insight required beyond direct formula application.
2. The mark, \(x\), scored by each student who sat a statistics examination is coded using
$$y = 1.4 x - 20$$
The coded marks have mean 60.8 and standard deviation 6.60
Find the mean and the standard deviation of \(x\).
\includegraphics[max width=\textwidth, alt={}, center]{8270bcae-494c-4248-8229-a72e9e84eab0-04_99_97_2613_1784}
Sub. 60.8 for \(y\) into a correct equation. Allow use of \(x\) or any other letter or expression for mean
\(= 57.7142\ldots\) awrt 57.7
A1
For awrt 57.7 or \(\frac{404}{7}\) (o.e.). Correct answer only is 2/2
\(\text{standard deviation} = \frac{6.60}{1.4}\) or \(6.60 = 1.4x\)
M1
Sub. 6.60 or 6.6 for \(y\) and ignoring the 20. Allow use of \(x\) or any other letter. \(6.60^2 = 1.4^2x^2\) is M0 until square root taken
\(= 4.7142\ldots\) awrt 4.71
A1
For awrt 4.71 or \(\frac{33}{7}\) (o.e.). Correct answer only is 2/2
# Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\text{mean} = \frac{60.8 + 20}{1.4}$ or $60.8 = 1.4x - 20$ | M1 | Sub. 60.8 for $y$ into a correct equation. Allow use of $x$ or any other letter or expression for mean |
| $= 57.7142\ldots$ awrt **57.7** | A1 | For awrt 57.7 or $\frac{404}{7}$ (o.e.). Correct answer only is 2/2 |
| $\text{standard deviation} = \frac{6.60}{1.4}$ or $6.60 = 1.4x$ | M1 | Sub. 6.60 or 6.6 for $y$ and ignoring the 20. Allow use of $x$ or any other letter. $6.60^2 = 1.4^2x^2$ is M0 until square root taken |
| $= 4.7142\ldots$ awrt **4.71** | A1 | For awrt 4.71 or $\frac{33}{7}$ (o.e.). Correct answer only is 2/2 |
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2. The mark, $x$, scored by each student who sat a statistics examination is coded using
$$y = 1.4 x - 20$$
The coded marks have mean 60.8 and standard deviation 6.60
Find the mean and the standard deviation of $x$.\\
\includegraphics[max width=\textwidth, alt={}, center]{8270bcae-494c-4248-8229-a72e9e84eab0-04_99_97_2613_1784}\\
\hfill \mbox{\textit{Edexcel S1 2014 Q2 [4]}}