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A box plot of some test marks has the five numbers: smallest 18, Q1 27, median 34, Q3 40 and…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A box plot of some test marks has the five numbers: smallest , Q1 , median , Q3 and largest .
- Find the range and the IQR.
- Between which marks does the middle half of the students lie?
- Is the upper whisker longer or shorter than the lower one? What might that tell you?
Need a reminder? The key ideaShow
Range = largest smallest. Q1 and Q3 are the medians of the lower and upper halves (leave the median out when the count is odd), and IQR .
The worked solution
Have you tried it?
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. Range. marks.
Step 2. IQR. marks.
Step 3. The middle half. Between and marks.
Step 4. The whiskers. The upper whisker runs from 40 to 61, that is 21 marks; the lower one from 18 to 27, only 9 marks. A few students scored much higher than the rest.
Answer: and marks; between and ; the upper whisker is longer.
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