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A biologist measures the wingspans of 10 butterflies caught in a meadow, a sample from a large…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A biologist measures the wingspans of 10 butterflies caught in a meadow, a sample from a large population. Her made-up notes say that the sum of the squared deviations from the sample mean is . Find the sample variance and the sample standard deviation. A student uses the population formula by mistake. What standard deviation does the student get?
Need a reminder? The key ideaShow
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 .
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. Sample variance. .
Step 2. Sample SD. mm.
Step 3. The mistake. mm.
Answer: , about mm, and 6 mm by mistake.
Watch out. The difference looks small, but with very small samples it grows. For two values, and give results that differ by a factor of about 1.4.
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