The back-to-back stem-and-leaf diagram shows the number of minutes played by two football league players, Player R and Player S, in \(11\) matches each this...
Question 1 Report
The back-to-back stem-and-leaf diagram shows the number of minutes played by two football league players, Player R and Player S, in \(11\) matches each this season.
| Player R | Stem | Player S |
|---|---|---|
| | 4 | 0 5 9 |
| 2 8 | 5 | 5 |
| 1 3 7 | 6 | 0 5 |
| 0 4 5 | 7 | 0 2 |
| 1 5 | 8 | 8 |
| 0 | 9 | 1 5 |
- Find the median minutes played for each player. (2)
- Find the interquartile range for each player. (2)
- State, with a reason, which player has more consistent playing time. (1)
Answer Details
A back-to-back stem-and-leaf diagram lists both players' minutes for the same match in one shared table, so each player's data can be read off, ordered, and then compared using the median and interquartile range in the usual way.
- Reading down the stems gives Player R's ordered minutes as \(52,58,61,63,67,70,74,75,81,85,90\), whose median (6th of 11 values) is \(70\) minutes; Player S's ordered minutes are \(40,45,49,55,60,65,70,72,88,91,95\), whose median is \(65\) minutes. [2 marks]
- For Player R, the lower quartile (3rd value) is \(61\) and the upper quartile (9th value) is \(81\), giving \(\text{IQR}=81-61=20\) minutes. For Player S, the lower quartile is \(49\) and the upper quartile is \(88\), giving \(\text{IQR}=88-49=39\) minutes. [2 marks]
- Player R has more consistent playing time, since his interquartile range of \(20\) minutes is much smaller than Player S's \(39\) minutes. [1 mark]
Player S actually has the lower median (\(65\) against Player R's \(70\)) yet the much larger spread, which shows that a smaller typical value does not imply more consistency; the two measures answer genuinely different questions about a player's game time.
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