| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2025 |
| Session | April |
| Marks | 5 |
| Topic | Measures of Location and Spread |
| Type | Reverse transformation: find original statistics |
| Difficulty | Moderate -0.8 This question tests standard results about linear transformations of data (how mean and standard deviation change under Y = aX + b). Part (a) requires reversing the transformation for the mean, part (b) applies the rule that SD scales by |a| only, and part (c) is simple algebra. All three parts are direct application of well-known formulas with no problem-solving or insight required—easier than average A-level statistics questions. |
| Spec | 5.02c Linear coding: effects on mean and variance |
A researcher has collected data on the heights of a sample of adults but has encoded the actual values using a linear transformation of the form $aX + b$, where $X$ represents the original height in centimetres.
Given the following information about the encoded data:
The mean of the encoded heights is 5.4 cm
The standard deviation of the encoded heights is 2.0 cm
The researcher knows that the transformation used was $0.2X - 30$
\begin{enumerate}[label=(\alph*)]
\item Find the mean of the original heights in the sample. [2]
\item Find the standard deviation of the original heights in the sample. [2]
\item If an encoded height value is 6.8, what was the original height in centimetres? [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2025 Q3 [5]}}