# Standard Deviation

Standard deviation measures how much a given set of numbers varies. It does not in any way reflect the average value of data or the quantity of the elements.

Thus, the numbers 1, 700, 62,000 and 1,000,000 would have a greater standard deviation than the numbers, 4, 5, 6, and 7.

The GRE does not test the formula for standard deviation nor does it expect test takers to remember “normal” distribution. It does, however, expect test takers to understand the concept. The test will frequently ask trick questions hoping that test takers will confuse standard deviation with mean or median value or range, such as those below for you to practice on.

## Practice

1. Data Set 1 has a range of 1-100. Data Set 2 has a range of 200-500. Is it possible to determine which set has a greater standard deviation?

2.

The chart above shows a normal distribution for hours spent watching television per week in Springfield, with a mean of 8 and a standard deviation of 6. What percentage of the population of Springfield watches fewer than 2 hours of television per week?

3.

Series I Series II
5, 6, 6, 7, 8, 10 1, 2, 3, 7, 15, 24

Which series has a greater standard deviation?

1. No, the difference in standard deviation cannot be determined

Standard deviation is a tool to measure how varied the results are from a given mean. It has nothing to do with the value of the numbers or the quantity of numbers in the set, except to the extent that these influence average distance from the mean.

2. 16%

Since the mean is 8 and the standard deviation is 6, 84% of the data sample will fall above 8-2, pursuant to the chart. The cutoff is represented by the “m - d” on the chart.

3. Set II has a greater standard deviation.

Standard deviation measures how close or far apart a set of numbers are from the mean. Set II is clearly more spread apart than Set I, thus, it has more standard deviation.

Again, the GRE does not expect test takers to know the standard deviation formula but it expects them to understand the concept.