Which Average Should the Team Report?
A Grade 6 basketball team records points scored in six games: 12, 15, 14, 13, 60, and 18. The coach wants a 'typical game' number for the school newsletter. One player computes the mean and gets 22. Another points out that no game was close to 22 and suggests the median. A third suggests the mode. The newsletter editor says the number must 'honestly describe a usual game' and asks the team to justify whichever measure they choose. The 60 came from a tournament game against much weaker opponents.
1. Calculate the mean, median, and mode, showing your work, and explain how the 60 affects each measure.
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Mean: (12 + 15 + 14 + 13 + 60 + 18) ÷ 6 = 132 ÷ 6 = 22.
Median: order the data: 12, 13, 14, 15, 18, 60. With six values, average the two middle ones: (14 + 15) ÷ 2 = 14.5.
Mode: every value appears once, so there is no mode.
The 60 is an outlier. It pulls the mean up from the cluster of 12–18 to 22, a value no game actually reached. The median depends on position, not size, so moving the 60 higher would not change the median at all; it stays 14.5, right in the middle of the usual scores. The mode is useless here because no score repeats.
2. Recommend a measure for the newsletter and justify it using the data and the editor's requirement.
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Recommend the median, 14.5 points.
The editor wants a number that honestly describes a usual game. Five of six games fall between 12 and 18, and the median 14.5 sits inside that cluster. The mean of 22 is inflated by a single unusual tournament game and would mislead readers into expecting about 22 points per game, which happened only once. The mode cannot be used because no value repeats.
A complete justification notes the trade-off: the mean uses every value and is useful when data are balanced, but it is sensitive to outliers. Here the outlier is real but unrepresentative, so the median better answers 'what is a typical game.' Mentioning that the 60 is genuine data, not an error, shows the choice is about purpose, not about deleting inconvenient numbers.