Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A fruit stall weighs nine apples, in grams: , and . These are made-up data, and one value is clearly a slip: the true mass was 163 g. Find the mean and the median with the slip. Then correct the slip and find them again. Which average was misled by the slip, and what would the fence rule have said about 1630 g?
The fences are 1.5 IQR beyond the quartiles; a value beyond a fence is an outlier.
Check an outlier for a mistake before you do anything else.
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. With the slip. The total is 2889 g, so the mean is . Sorted, the masses are , , so the median is 158 g.
Step 2. After the correction. The total is g, so the mean is . The median is still the 5th value, 158 g.
Answer: with the slip, a mean of 321 g and a median of 158 g; after it, 158 g and 158 g.
What it shows. The mean was misled: 321 g is twice the mass of any real apple. The median did not move. With the slip, g and g, so the upper fence is g. The rule flags 1630 g as an outlier, and a look at it shows a slip.
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