Example of Computing the Standard Deviation

Estimating Population Standard Deviation

Arrange the procedural steps for computing the standard deviation of a sample in the correct order.

In the formula for calculating a sample's standard deviation ($SD = \sqrt{\frac{\sum (X-M)^2}{N}}$), what is the primary logical reason for squaring the difference between each score ($X$) and the mean ($M$)?

Analyze the mathematical structure of the standard deviation formula ($SD = \sqrt{\frac{\sum (X-M)^2}{N}}$) and match each component with the specific logical function it serves in the process of quantifying psychological data variability.

When evaluating the functional purpose of the standard deviation formula ($SD = \sqrt{\frac{\sum (X-M)^2}{N}}$), the final square root is considered a critical step for interpretability because it returns the measure of variability to the same units as the original scores ($X$).

In the formula used to calculate the standard deviation of a sample, $SD = \sqrt{\frac{\sum (X-M)^2}{N}}$, what does the symbol $N$ represent?

Match each change in a psychological dataset's distribution to its corresponding effect on the results of the standard deviation formula ($SD = \sqrt{\frac{\sum (X-M)^2}{N}}$).

In a psychology study measuring sleep duration, a researcher finds that for a sample of $N = 10$ participants, the sum of the squared deviations from the mean—$\sum (X - M)^2$—is 360. Based on the formula $SD = \sqrt{\frac{\sum (X-M)^2}{N}}$, the standard deviation for this sample is _____.