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Why is the standard deviation of the distribution of sample means smaller than the standard deviation of the population from which it came? Select all that apply.

Why is the standard deviation of the distribution of sample means smaller than the standard deviation of the population from which it came? Select all that apply.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Why is the standard deviation of the distribution of sample means smaller than the standard deviation of the population from which it came? Select all that apply. According to the central limit theorem, we divide the population standard deviation o by the square root of the sample size n, so as n gets bigger the quotient gets smaller. Since we are only graphing the averages of the samples, extremes like the minimum and maximum of each sample are not present, making the standard deviation of the sample means smaller than the standard deviation of the population. The standard deviation of the distribution of sample means is smaller than the standard deviation of the population because a sample is always small than the population.
Transcribed Image Text:Why is the standard deviation of the distribution of sample means smaller than the standard deviation of the population from which it came? Select all that apply. According to the central limit theorem, we divide the population standard deviation o by the square root of the sample size n, so as n gets bigger the quotient gets smaller. Since we are only graphing the averages of the samples, extremes like the minimum and maximum of each sample are not present, making the standard deviation of the sample means smaller than the standard deviation of the population. The standard deviation of the distribution of sample means is smaller than the standard deviation of the population because a sample is always small than the population.
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