Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A shop records the number of customers who came in on different days: and . The manager wants the five-number summary, the interquartile range and a check for unusually busy or quiet days. Use the rule that leaves out the median when the number of values is odd. Find , , the interquartile range, the upper fence, and the number of outliers.
and are the medians of the lower and the upper half. . The fences are and .
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 median. The sixth value is .
Step 2. The quartiles. The lower half is , with median . The upper half is , with median .
Step 3. The IQR. .
Step 4. The fences. The upper fence is . The lower fence is .
Step 5. Outliers. The smallest value is above and the largest value is below . There are no outliers.
Answer: , , , upper fence , and no outliers.
Check. looks large, but it is inside the fence.
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