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A weather station records the daily rainfall, in millimetres, on twelve days of a month: 2, 3, 3…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A weather station records the daily rainfall, in millimetres, on twelve days of a month: and . The last value is from one heavy storm. A climate student wants to draw a box plot, and she also wants to know how much the storm affects the mean. She will use the rule that finds the quartiles as the medians of the two halves, and the fences at times the interquartile range from the quartiles. A value outside the fences is plotted as a cross, and the whisker ends at the last value inside the fences. Find , , the upper fence, the value at which the upper whisker ends, and the mean rainfall of the other eleven days.
Need a reminder? The key idea
The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The halves. The lower half is , so . The upper half is , so .
Step 2. The fence. . The upper fence is mm. The value is above it, so it is an outlier.
Step 3. The whisker. The largest value not above is . The upper whisker ends at mm.
Step 4. The mean without the storm. The other eleven values add up to , so the mean is mm. With the storm the mean is mm.
Answer: mm, mm, upper fence mm, whisker end mm, mean without the storm mm.
What it means. One storm raises the mean by about mm, but it does not move the quartiles at all.
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