# Statistics

Every GMAT exam contains a number of statistics questions. Which topics are included?

• Averages

• Medians

• Variance and standard deviation

• Combinatorics

• Probability

On this page you can view examples of these types of questions, and also login to our advanced exercise program to practice statistics questions for free.

Here is an example of a statistics question from the quantitative section of the GMAT.

Set S contains the numbers 11, 14, 17, and X. Which of the following could be the median of set S?

i. 12

ii.13

iii.14

(A) Only ii

(B) Only iii

(C) i and ii

(D) ii and iii

(E) i and ii and iii

__:__

**Solution**
Since there are four numbers in the given set, the median will be equal to the average of the two middle numbers (after we sort the numbers from smallest to largest). And so, the median depends on the value of X:

• If X is smaller than or equal to 11, the median will be the average of 14 and 11, meaning 12.5

• If X is greater than or equal to 17, the median will be the average of 14 and 17, meaning 15.5

• If X is between 11 and 17, the median will be the average of X and 14, which can be anywhere between the numbers 12.5 and 15.5

• It's important to notice that the numbers are not defined as different from each other and so X could also be equal to 14. In this case, the median will be the average of 14 and 14 which is 14.

We can see that the median could be any number that is equal to or greater than 12.5 or equal to or smaller than 15.5.

And so, the answer is D.

**Here is another example of a statistics question from the quantitative section of the GMAT:**
Danny, Mike, Suzy, Shrutika and Wung are sitting on a bench for a group photo. If Wung and Suzy must sit next to each other, how many different seating arrangements are possible?

• 24

• 48

• 72

• 96

• 120

**Solution:**
We can see that this is a combinatorics question, which asks us to arrange objects (or in this case, people).

There are X! ways to arrange X objects in a row. If the question did not include the restriction regarding Suzy and Wung, the answer would have be 5!, meaning 120.

However, the question is made slightly more complicated by stating that Suzy and Wung must sit next to each other. For this purpose, we will treat with Suzy and Wung as if they are one object – that means, at the moment we need to arrange 4 objects, i.e. 4! possibilities. Next we will multiply this amount by the number of possible seating arrangements between Suzy and Wung which is 2! (in any arrangement Suzy can sit to Wung's left or to his right). Let's multiply: 4! X 2! = 24 x 2= 48

The answer is 48 (B)

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