SPS SPS SM Statistics 2025 April — Question 5 13 marks

Exam BoardSPS
ModuleSPS SM Statistics (SPS SM Statistics)
Year2025
SessionApril
Marks13
TopicMeasures of Location and Spread
TypeFind median and quartiles from stem-and-leaf diagram
DifficultyEasy -1.3 This is a straightforward statistics question testing basic descriptive statistics from stem-and-leaf diagrams. All parts involve standard procedures: finding median/quartiles, calculating mean/SD from listed data, and recalling textbook advantages of different measures. No problem-solving or novel insight required—purely routine statistical calculations and recall of standard comparisons between measures of spread.
Spec2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02i Select/critique data presentation
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
  1. State the median reaction time. [1]
  2. Calculate the interquartile range of these reaction times. [2]
  3. Find the mean and standard deviation of these reaction times. [3]
  4. State one advantage of using a stem-and-leaf diagram to display this data rather than a frequency table. [1]
  5. 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: a. the median b. the mean c. the standard deviation [4]
  6. Explain why the interquartile range might be preferred to the standard deviation as a measure of spread in this context [2]
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:
a. the median
b. the mean
c. the standard deviation [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 SM Statistics 2025 Q5 [13]}}
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