Graduate Management Admission Test (GMAT) Practice Test

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What is the formula for calculating standard deviation?

Average of all terms
Square root of average squared difference from the mean
Sum of differences from the mean
Median of the set

The correct answer is: Square root of average squared difference from the mean

The formula for calculating standard deviation is the square root of the average squared difference from the mean. This involves a few key steps: first, you calculate the mean (average) of the data set. Then, for each value in the data set, you determine the difference from the mean and square that difference. These squared differences are averaged (by summing them up and dividing by the number of data points, usually n for a population standard deviation, or n-1 for a sample standard deviation). Finally, taking the square root of this average gives the standard deviation. This method effectively quantifies the dispersion of data points relative to the mean, allowing for insights into the variability within the data set. This is why the correct choice clearly encapsulates the fundamental process for deriving standard deviation.