Date | May 2022 | Marks available | 1 | Reference code | 22M.2.SL.TZ2.5 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 2 |
Command term | State | Question number | 5 | Adapted from | N/A |
Question
A random sample of nine adults were selected to see whether sleeping well affected their reaction times to a visual stimulus. Each adult’s reaction time was measured twice.
The first measurement for reaction time was taken on a morning after the adult had slept well. The second measurement was taken on a morning after the same adult had not slept well.
The box and whisker diagrams for the reaction times, measured in seconds, are shown below.
Consider the box and whisker diagram representing the reaction times after sleeping well.
State the median reaction time after sleeping well.
Verify that the measurement of seconds is not an outlier.
State why it appears that the mean reaction time is greater than the median reaction time.
Now consider the two box and whisker diagrams.
Comment on whether these box and whisker diagrams provide any evidence that might suggest that not sleeping well causes an increase in reaction time.
Markscheme
(s) A1
[1 mark]
(s) (A1)
substituting their into correct expression for upper fence (A1)
(s)
R1
so (s) is not an outlier AG
[3 marks]
EITHER
the median is closer to the lower quartile (positively skewed) R1
OR
The distribution is positively skewed R1
OR
the range of reaction times below the median is smaller than the range of reaction times above the median R1
Note: These are sample answers from a range of acceptable correct answers. Award R1 for any correct statement that explains this.
Do not award R1 if there is also an incorrect statement, even if another statement in the answer is correct. Accept a correctly and clearly labelled diagram.
[1 mark]
EITHER
the distribution for ‘not sleeping well’ is centred at a higher reaction time R1
OR
The median reaction time after not sleeping well is equal to the upper quartile reaction time after sleeping well R1
OR
of reaction times are seconds after sleeping well, compared with after not sleeping well R1
OR
the sample size of is too small to draw any conclusions R1
Note: These are sample answers from a range of acceptable correct answers. Accept any relevant correct statement that relates to the median and/or quartiles shown in the box plots. Do not accept a comparison of means. Do not award R1 if there is also an incorrect statement, even if another statement in the answer is correct.
Award R0 to “correlation does not imply causation”.
[1 mark]
Examiners report
Parts (a) and (b) were generally known, but answers to parts (c) and (d) showed poor understanding of interpreting data. Many students thought they could find the mean by considering only the end points. Others assumed it would be halfway between the quartiles. When it came to evidence, many were far too quick to say the diagrams 'proved' something. Most compared only the medians and thought that was sufficient evidence, completely ignoring the fact the median only represented one data point. Others just compared the maximum and minimum. A few commented correctly that 9 subjects was too small a sample to prove anything.