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## Standard Deviation on the GRE

GRE Standard deviation is a commonly used term when discussing statistics and probability. We do also come across a couple of standard deviation questions on the GRE. Let’s understand, what standard deviation means.

Standard deviation of a set or a list of values is the degree of spread of the data around the mean. It is represented by the Greek letter sigma (σ) and is calculated using the formula

Let’s take an example to understand standard deviation

Example 1:

Consider set A= {1, 3, 5} and set B= {2, 4, 6}. What can we say about the standard deviations of the two sets?

Interpretation:

In set A, the value 1 and 5 are two points below and above the mean 3; i.e. the spread is 2 points around the mean. Also in set B, the spread is 2 points around the mean. Since the degree of spread is same for both the sets, irrespective of different means and different values, we can say that the standard deviations GRE of set A and set B are equal.

On GRE, we might see a question relating to standard deviation, which most probably will be a Quantitative Comparison question.

Example 2:

Set A= {1, 3, 5, 7, 9}

Set B= {2, 4, 6, 8}

Quantity A                                                                                        Quantity B

Standard Deviation of Set A                                                               Standard Deviation of Set B

1. Quantity A is greater.
2. Quantity B is greater.
3. Two quantities are equal.
4. The relationship cannot be determined from the information given.

Solution:

In set A, we can see that the mean is 5 and the spread is 4 points below and above the mean.

In set B, we can see that the mean is 5 but the spread is 3 points below and above the mean.

Therefore, the standard deviation of Set A is greater than that of Set B.

Here is another way to look at this. Reckon that {3, 5, 7, 9} and {2, 4, 6, 8} have the same standard deviation. Set A has one more value outside the range of {3, 5, 7, 9}. This will increase the spread and, hence, the standard deviation.

Conclusion: The more closely packed are the values around the mean, the smaller the standard deviation. The greater the standard deviation, farther away are the values from the mean.

Minimum possible standard deviation of any list is 0 — when all the values are the same — because there is no spread around the mean.

Next time, we will talk about GRE Standard Deviation for a Normally Distributed data set.

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