**How to approach statistics problems on the UMAT exam:**

Frequently a feature of UMAT multi choice, understanding the language of statistics and how to answer those questions involving statistics on the UMAT exam is essential for UMAT success. Below, we have explained, as succinctly as possible, what you need to know in order to answer this style of UMAT question.

Statistics is the study of the patterns and relationships of numbers and data. There are four main concepts that may appear on the UMAT exam.

Median

Median

When a set of numbers is arranged in order of size, the **median is the middle number**.

For example, the median of the set {8, 9, 10, 11, 12} is 10 because it is the middle number.

In this case, the median is also the mean (average). But this is usually not the case.

For example, the median of the set {8, 9, 10, 11, 17} is 10 because it is the middle number, but the mean is

11 =(8+9+10+11+17)/5.

**If a set contains an even number of elements, then the median is the average of the two middle elements.**

For example, the median of the set {1, 5, 8, 20} is 6.5 = [(5+8)/2].

**Sample UMAT style question: **What is the median of 0, -2, 256, 18, ?2?

Arranging the numbers from smallest to largest (numbers could be arranged from the largest to smallest; the answer would still be the same), we get -2, 0, ?2, 18, 256.

The median is the middle number, ?2.

Mode

Mode

The **mode** is **the number or numbers that appear most frequently in a set**. Note that this definition allows a set of numbers to have **more than one mode.**

** Sample UMAT style question: **What is the mode of 3, -4, 3, 7, 9, 7.5?

The number 3 is the mode because it is the only number that is listed more than once.

** Sample UMAT style question: **What is the mode of 2, pi, 2, -9, pi, 5?

Both 2 and pi are modes because each occurs twice, which is the greatest number of occurrences for any number in the list.

Range

Range

The **range** is the distance between the smallest and largest numbers in a set. To calculate the range, merely subtract the smallest number from the largest number.

** Sample UMAT style question: **What is the range of 2, 8, 1, -6, pi, 1/2?

The largest number in this set is 8, and the smallest number is -6. Hence, the range is 8 – (-6) = 8 + 6=14.

Standard Deviation

Standard Deviation

On the UMAT exam, you are not expected to know the definition of standard deviation. However, you may be presented with the definition of standard deviation and then be asked a question based on this definition. To make sure we cover all possible bases, we’ll briefly discuss this concept.

**Standard deviation **measures **how far the numbers in a set vary from the set’s mean.** If the numbers are scattered far from the set’s mean, then the standard deviation is large. If the numbers are bunched up near the set’s mean, then the standard deviation is small.

** Sample UMAT style question: **Which of the following sets has the larger standard deviation?

A= {1, 2, 3, 4, 5}

B = {1, 4, 15, 21, 27}

All the numbers in Set A are within 2 units of the mean, 3. All the numbers in Set B are greater than 5 units from the mean, 15. Hence, the standard deviation of Set B is greater.

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