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# Arithmetic for Praxis I: Pre-Professional Skills Test Study Guide (page 6)

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### Statistics

Statistics is the field of mathematics that deals with describing sets of data. Often, we want to understand trends in data by looking at where the center of the data lies. There are a number of ways to find the center of a set of data.

### Mean

When we talk about average, we usually are referring to the arithmetic mean (usually just called the mean). To find the mean of a set of numbers, add all of the numbers together and divide by the quantity of numbers in the set.

average = (sum of set) ÷ (quantity of set)
Examples
Find the average of 9, 4, 7, 6, and 4.

The mean, or average, of the set is 6.
(Divide by 5 because there are five numbers in the set.)

### Median

Another center of data is the median. It is literally the center number if you arrange all the data in ascending or descending order. To find the median of a set of numbers, arrange the numbers in ascending or descending order and find the middle value.

• If the set contains an odd number of elements, then simply choose the middle value.
Examples
Find the median of the number set: 1, 5, 4, 7, 2.
•

First arrange the set in order—1, 2, 4, 5, 7—and then find the middle value. Because there are five values, the middle value is the third one: 4. The median is 4.

• If the set contains an even number of elements, simply average the two middle values.
Examples
Find the median of the number set: 1, 6, 3, 7, 2, 8.
•

First arrange the set in order—1, 2, 3, 6, 7, 8—and then find the middle values, 3 and 6. Find the average of the numbers 3 and 6: . The median is 4.5.

### Mode

Sometimes when we want to know the average, we just want to know what occurs most often. The mode of a set of numbers is the number that appears the greatest number of times.

Examples
For the number set 1, 2, 5, 9, 4, 2, 9, 6, 9, 7, the number 9 is the mode because it appears the most frequently.

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