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Fifteen values from a made-up science experiment have a mean of 40 and a median of 38…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Fifteen values from a made-up science experiment have a mean of 40 and a median of 38. In order, the eighth value is 38 and the ninth is 41. A sixteenth reading of 100 is added, and it is larger than all the others. Find the new mean and the new median. Which average moved more?
Need a reminder? The key ideaShow
The mean is the balance point and follows a long tail; the median is the middle value and hardly moves. Usually a right skew gives mean > median and a left skew gives mean < median. Report the median for skewed data.
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 new mean. The old total is . The new total is . So the new mean is .
Step 2. The new median. The new value is the largest, so the order of the first fifteen stays. With 16 values, the median is the mean of the eighth and ninth values: .
Answer: The new mean is and the new median is .
Compare. The mean rose by , the median by only . One large value moves the mean much more.
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