A land surveyor measured the lengths, in metres, of 9 fence sections around a paddock, shown in the table below. The fencing contractor uses these figures t...
Question 1 Report
A land surveyor measured the lengths, in metres, of 9 fence sections around a paddock, shown in the table below. The fencing contractor uses these figures to plan the next repair visit. Sections shorter than the paddock's minimum boundary length will be replaced first.
| Section | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Length (m) | 18 | 22 | 15 | 25 | 19 | 21 | 17 | 23 | 20 |
- Find the median length (2)
- Find the interquartile range of the fence lengths (3)
Answer Details
This question tests calculating a median and an interquartile range from a raw list of fence lengths.
- Sorting the nine lengths: 15, 17, 18, 19, 20, 21, 22, 23, 25. With 9 values, the median is the middle (5th) value, 20 m [2].
- Excluding the median, the lower four values are 15, 17, 18, 19, giving lower quartile \( \frac{17+18}{2}=17.5 \) m. The upper four values are 21, 22, 23, 25, giving upper quartile \( \frac{22+23}{2}=22.5 \) m. The interquartile range is \[ 22.5-17.5 = \] 5 m [3].
With 9 values, each quartile is itself the average of two values once the median has been set aside, since the remaining four values in each half have no single middle value of their own.
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