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A shop sells these items on one day, with the prices [20, 25, 25, 30, 22, 28, 400]…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A shop sells these items on one day, with the prices [20, 25, 25, 30, 22, 28, 400]. Find the mean, the median and the mode. Which one describes a normal sale best, and why?
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.
Plan. Use the three tools of statistics.
- The sum is 550, and 550 divided by 7 is about 78.57, the mean.
- In order the data is 20, 22, 25, 25, 28, 30, 400, so the middle (fourth) value is 25, the median.
- The value 25 appears twice, so the mode is 25.
The one sale of 400 pulls the mean up to 78.57, a price at which no normal sale was made. The median and the mode, both 25, describe a normal sale.
Check. Remove the 400 and run it again. The mean drops to 25.0, close to the median.
Answer: mean 78.57, median 25, mode 25. The median (or the mode) describes a normal sale, because the mean is pulled by the one very big value.
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