Case 3 uses Sd to measure dispersion around the mean. Which statement is true?

Case 3 uses Sd to measure dispersion around the mean. Which statement is true?

• A. Sd is the standard deviation
• B. Sd is the standard error of the mean
• C. Sd is the variance
• D. Sd is the range

Answer: (A)

Dispersion around the mean is described by the standard deviation. It measures, on average, how far individual values stray from the average value. For a sample, the standard deviation is the square root of the average squared deviations from the sample mean (using n−1 in the denominator). This differs from the standard error of the mean, which describes how precisely the sample mean estimates the true mean and equals the standard deviation divided by the square root of the sample size. It’s also not the variance (which is the square of the standard deviation) and not the range (the simple max minus min). Since Case 3 uses Sd to describe spread around the mean, Sd being the standard deviation is the correct interpretation.

Dispersion around the mean is described by the standard deviation. It measures, on average, how far individual values stray from the average value. For a sample, the standard deviation is the square root of the average squared deviations from the sample mean (using n−1 in the denominator). This differs from the standard error of the mean, which describes how precisely the sample mean estimates the true mean and equals the standard deviation divided by the square root of the sample size. It’s also not the variance (which is the square of the standard deviation) and not the range (the simple max minus min). Since Case 3 uses Sd to describe spread around the mean, Sd being the standard deviation is the correct interpretation.