| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2025 |
| Session | April |
| Marks | 13 |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from stem-and-leaf diagram |
| Difficulty | Moderate -0.8 This is a straightforward descriptive statistics question requiring routine calculations from a stem-and-leaf diagram. All parts involve standard procedures (finding median, IQR, mean, standard deviation) with no problem-solving or novel insight required. The data is already organized, making calculations mechanical. This is easier than average A-level content, though the multi-part nature and calculator work prevent it from being trivial. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
In a study of reaction times, 25 participants completed a test where their reaction times (in milliseconds) were recorded. The results are shown in the stem-and-leaf diagram below:
20 | 3 5 7 9
21 | 0 2 5 6 8
22 | 1 3 4 5 7 9
23 | 0 2 5 8
24 | 1 4 6 7
25 | 2 5
Key: 21 | 0 represents a reaction time of 210 milliseconds
\begin{enumerate}[label=(\alph*)]
\item State the median reaction time. [1]
\item Calculate the interquartile range of these reaction times. [2]
\item Find the mean and standard deviation of these reaction times. [3]
\item State one advantage of using a stem-and-leaf diagram to display this data rather than a frequency table. [1]
\item One participant completed the test again and recorded a reaction time of 195 milliseconds. Add this result to the stem-and-leaf diagram and state the effect this would have on:
\begin{enumerate}[label=(\roman*)]
\item the median
\item the mean
\item the standard deviation
\end{enumerate}
[4]
\item Explain why the interquartile range might be preferred to the standard deviation as a measure of spread in this context [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2025 Q2 [13]}}