A water treatment plant recorded the volume of water used each day over one month, in thousands of litres. The box plot summarises the results. 100 140 180 ...
Question 1 Report
A water treatment plant recorded the volume of water used each day over one month, in thousands of litres. The box plot summarises the results.
- Write down the median daily volume shown by the box plot. (1)
- Work out the interquartile range of the daily volumes. (2)
- Work out the range of the daily volumes. (1)
- The plant sets a daily target of 200 thousand litres. State, with a reason taken from the box plot, whether more than half of the days reached this target. (2)
Answer Details
The box plot's five marked values, \(120, 150, 175, 210, 260\) thousand litres, give the minimum, lower quartile, median, upper quartile and maximum daily volume used.
- The median is the line inside the box: \(175\) thousand litres. [1 mark]
- Interquartile range = upper quartile minus lower quartile: \(210-150=60\) thousand litres. [2 marks]
- Range = maximum minus minimum: \(260-120=140\) thousand litres. [1 mark]
- The median, \(175\), is below the target of \(200\) thousand litres. Since the median splits the data exactly in half, at least half of the days used less than the target, so fewer than half of the days reached it. [2 marks]
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