| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2026 |
| Session | January |
| Marks | 10 |
| Topic | Measures of Location and Spread |
| Type | Calculate variance from summary statistics |
| Difficulty | Moderate -0.3 This is a straightforward multi-part statistics question requiring basic calculations (range, IQR, mean, standard deviation from given summations) and conceptual understanding of how additional data points affect measures of location and spread. All techniques are standard A-level content with no novel problem-solving required, though part (f) requires some thought about balancing conditions. Slightly easier than average due to the routine nature of most parts. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers |
2.
Each member of a group of 27 people was timed when completing a puzzle.\\
The time taken, $x$ minutes, for each member of the group was recorded.\\
These times are summarised in the following box and whisker plot.\\
\includegraphics[max width=\textwidth, alt={}, center]{fdff6575-679e-4d25-ad43-e9d343c1746f-06_346_1383_427_278}
\begin{enumerate}[label=(\alph*)]
\item Find the range of the times.
\item Find the interquartile range of the times.
For these 27 people $\sum x = 607.5$ and $\sum x ^ { 2 } = 17623.25$
\item calculate the mean time taken to complete the puzzle,
\item calculate the standard deviation of the times taken to complete the puzzle.
Taruni defines an outlier as a value more than 3 standard deviations above the mean.
\item State how many outliers Taruni would say there are in these data, giving a reason for your answer.
Adam and Beth also completed the puzzle in $a$ minutes and $b$ minutes respectively, where $a > b$.\\
When their times are included with the data of the other 27 people
\begin{itemize}
\item the median time increases
\item the mean time does not change
\item Suggest a possible value for $a$ and a possible value for $b$, explaining how your values satisfy the above conditions.
\item Without carrying out any further calculations, explain why the standard deviation of all 29 times will be lower than your answer to part (d).
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2026 Q2 [10]}}