10 students were randomly selected from each class to form 6 samples

MATHEMATICS · Multi-part · AP · AP Statistics · Sampling Distributions · Sampling Distributions

Problem

10 students were randomly selected from each class to form 6 samples. Their responses to the survey are shown below:
<i>Sample 1:</i>101416916151521921
<i>Sample 2:</i>1191116161310122116
<i>Sample 3:</i>121014713112120159
<i>Sample 4:</i>20191919131922151019
<i>Sample 5:</i>1913231117414211311
<i>Sample 6:</i>191116681310222011
(a) Calculate the *sample* statistics ss and s2s^2 for each sample. (b) Calculate the *population* statistics σ\sigma and σ2\sigma^2 for each sample. (c) Which set of estimates from a and b are generally closer to the true population variance and standard deviation? (d) Does your answer to c explain why we have different variance and standard deviation formulae for a sample as opposed to a population?

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