Reporting a typical netball score
The school netball team played nine matches this season. The number of goals they scored in each match was:
18, 20, 22, 22, 25, 26, 30, 31, 48
The coach must write a short report for the sports committee and wants to quote one 'typical score' to show how the team usually performed. A parent claims the figure of 48 was recorded wrongly and should be 28, but the original score sheet cannot be found before the report is due. The committee will use the report to decide whether the team needs a new shooting coach.
1. Calculate the mean, median and mode of the nine scores. Which one should the coach quote as the typical score, and why?
Read the worked answer
Mean: sum = 18 + 20 + 22 + 22 + 25 + 26 + 30 + 31 + 48 = 242
Mean = 242 ÷ 9 = 26.9 goals (to 1 d.p.)
Median: the scores are already in order; the 5th value is 25 goals.
Mode: 22 appears twice, all others once, so the mode is 22 goals.
Which to quote: the median (25) or the mode (22). Eight of the nine scores lie between 18 and 31, so 48 is an outlier - possibly a genuine outstanding match, possibly the mis-recorded figure the parent mentions. That single value pulls the mean up to 26.9, above seven of the nine actual scores, so the mean overstates what the team 'usually' scores. The median is not affected by one extreme value and is therefore the safer summary; the coach should quote 25 and mention the 48 as a separate outstanding result rather than hide it.
2. A match is chosen at random from the nine. Find the probability that the team scored more than the median score.
Read the worked answer
The median is 25. 'More than the median' means a score strictly greater than 25:
26, 30, 31, 48 → 4 matches
The scores 18, 20, 22, 22 and 25 do not count, and 25 itself does not count because the question says more than, not at least.
Probability = 4/9 ≈ 0.444 (about 44%).
Note that if the parent's correction (48 → 28) were used, the median would still be 25 and the scores above it would be 26, 28, 30, 31, so the probability would be unchanged at 4/9. This is a further reason for preferring the median in the report.
3. Recalculate the mean using 28 instead of 48. State how the mean and the median change, and comment on whether the correction changes the coach's conclusion.
Read the worked answer
New sum = 242 − 48 + 28 = 222
New mean = 222 ÷ 9 = 24.7 goals (to 1 d.p.)
Change in mean: 26.9 − 24.7 = 2.2 goals lower.
New ordered list: 18, 20, 22, 22, 25, 26, 28, 30, 31. The 5th value is still 25, so the median does not change at all.
The mean falls by about 2.2 and now sits much closer to the median (25), which confirms that the original mean was being dragged upwards by the 48. The coach's conclusion should not change, because the recommendation rested on the median, which is the same under either version of the data. However, the report should state that one score is in dispute, since the committee is using the report to make a decision and should know that the mean could be 24.7 or 26.9 depending on how that entry is resolved.