SPS SPS FM Statistics 2025 April — Question 2 6 marks

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2025
SessionApril
Marks6
TopicMeasures of Location and Spread
TypeFind median and quartiles from stem-and-leaf diagram

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: \(20 \mid 3579\)
\(21 \mid 02568\)
\(22 \mid 134579\)
\(23 \mid 0258\)
\(24 \mid 1467\)
\(25 \mid 25\) Key: 21 | 0 represents a reaction time of 210 milliseconds
  1. State the median reaction time.
  2. Calculate the interquartile range of these reaction times.
  3. Find the mean and standard deviation of these reaction times.
  4. State one advantage of using a stem-and-leaf diagram to display this data rather than a frequency table.
  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:
    i) the median
    ii) the mean
    ii) the standard deviation
    [0pt] [4]
  6. Explain why the interquartile range might be preferred to the standard deviation as a measure of spread in this context
    [0pt] [2]