Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A school football team scores and goals in its five matches of a made-up season. These five matches are the whole season, the group we care about. Find the mean, the MAD and the population standard deviation . Then, for comparison, find the sample standard deviation . Give decimals to two places.
Deviations from the mean add up to zero. The MAD averages their sizes; the variance averages their squares. Population (whole group): divide by . Sample: divide by .
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 mean. goals.
Step 2. The MAD. The distances from 3 are , with total 12. MAD goals.
Step 3. Population SD. The squares are , with total 40. goals.
Step 4. Sample SD. goals.
Answer: mean 3, MAD , , goals.
Check. The SD is larger than the MAD, because the match with 8 goals has a big deviation, and squaring makes it count more.
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