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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 \( \sigma \) 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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