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A farm packs eggs in baskets and records how many eggs each basket holds…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A farm packs eggs in baskets and records how many eggs each basket holds. Twenty baskets are counted.
| Eggs in a basket | 3 | 6 | 9 | 12 | 15 |
|---|---|---|---|---|---|
| Number of baskets | 4 | 5 | 6 | 3 | 2 |
Find the median number of eggs in a basket, the mean deviation about the median, and the mean deviation about the mean.
Need a reminder? The key ideaShow
The mean deviation about a centre is . The range is the largest value minus the smallest. Divide a spread by its centre to get a coefficient.
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 median. The running totals are . The th and th values both lie in the group of eggs, so the median is .
Step 2. About the median. The distances from are . Multiply by the frequencies: . So eggs.
Step 3. The mean. , so eggs.
Step 4. About the mean. The distances from are . Then , and eggs.
Answer: median eggs, mean deviation eggs about the median and eggs about the mean.
Check. The mean deviation is smaller about the median than about the mean, as it should be.
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