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The finishing times of 40 people in a made-up 5 km fun run are grouped into bins 5 minutes wide…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The finishing times of 40 people in a made-up 5 km fun run are grouped into bins 5 minutes wide from 20 to 65 minutes. The heights are 4, 9, 5, 1, 0, 2, 7, 8 and 4. How many people finished between 35 and 45 minutes? Estimate the mean time by using the middle of each bin, to two decimal places. In which bin does the estimate fall, and how many people finished in that bin? What does this tell you about the mean of a bimodal distribution?
Need a reminder? The key ideaShow
Describe a distribution by its shape, centre, spread and unusual features. Skew is named after the long tail. Two peaks often mean two groups mixed together. A gap or an outlier deserves a reason.
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. The valley. The bins 35 to 40 and 40 to 45 hold person.
Step 2. The estimate of the mean. The middles are minutes. The sum of middle times height is minutes. So the estimate is minutes.
Step 3. Where it falls. In the bin 40 to 45 minutes, which holds 0 people.
Answer: 1 person, about minutes, a bin with 0 people.
What it means. Two groups are mixed: runners near 27 minutes and walkers near 55 minutes. The mean sits between them, at a time that nobody took. For a bimodal distribution, describe each group on its own.
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