A quality inspector at a building site tested the mass, in kilograms, of 12 concrete blocks from one batch, marking each result on a dot plot before the loa...
Question 1 Report
A quality inspector at a building site tested the mass, in kilograms, of 12 concrete blocks from one batch, marking each result on a dot plot before the load could be signed off.
- Write down the mode of the masses. (1)
- Find the median mass. (2)
- Work out the range of the masses. (1)
- Work out the interquartile range of the masses. (2)
- The batch is accepted only if the interquartile range is at most 2.5 kg. State, with a reason, whether this batch should be accepted. (1)
Answer Details
Reading a dot plot means counting the stacked dots above each mass to rebuild the twelve individual readings: \(18, 19, 19, 20, 20, 20, 21, 21, 22, 23, 23, 24\) kg.
- The tallest stack of dots is above \(20\) kg, with three blocks recorded at that mass, so the mode is \(20\) kg. [1 mark]
- With 12 values the median is the mean of the 6th and 7th values: \((20+21)\div2=20.5\) kg. [2 marks]
- Range = \(24-18=6\) kg. [1 mark]
- The lower quartile is the mean of the 3rd and 4th values, \((19+20)\div2=19.5\) kg. The upper quartile is the mean of the 9th and 10th values, \((22+23)\div2=22.5\) kg. Interquartile range = \(22.5-19.5=3.0\) kg. [2 marks]
- The batch's interquartile range of \(3.0\) kg is greater than the \(2.5\) kg limit, so this batch should not be accepted. [1 mark]
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