Example 3: standard deviation as a refinement of margin of error
note that the margin of error is measuring how spread out the sample means are relative to the value of the actual population mean. from previous lessons, you know that the standard
deviation is a good measure of spread. so, rather than producing a visual estimate for the margin of error from the distribution of sample means, another approach is to use the standard
deviation of the sample means as a measure of spread. for example, the standard deviation of the 50 sample means in the example above is 1.7. note that if you double 1.7,
you get a value for margin of error close to the visual estimate of 3.5.
another way to estimate margin of error is to use two times the standard deviation of a distribution of sample means.
for the above example, because 2(1.7) = 3.4, the refined margin of error (based on the standard deviation of sample means) is 3.4 rating points.
an interpretation of the margin of error is that plausible values for the population mean rating are from 7.5 − 3.4 to 7.5 + 3.4 (i. e., 4.1 to 10.9 rating points).