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# Measures of Central Tendency Study Guide: GED Math (page 2)

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Updated on Mar 23, 2011

Practice problems for these concepts can be found at:

Data Analysis, Statistics, and Probability Practice Problems: GED Math

### Measures of Central Tendency

Statistics are everywhere—in news reports, in sports, and on your favorite websites. Mean, median, and mode are three common statistics that give information on a group of numbers. They are called measures of central tendency because they are different ways of finding the central trend in a group of numbers.

### Finding the Mean

Mean is just another word for average. The mean, or average, is one of the most useful and common statistics. You probably already average your grades at school regularly, so you may already know the basic steps to finding the mean of a set of numbers.

Step 1   Add all the numbers in the list.

Step 2   Count how many numbers are in the list.

Step 3   Divide the sum (the result of step 1) by the number of numbers (the result of step 2).

Another way to think about the mean is in the form of this equation:

Example

Find the mean of the following set of numbers: 5, 7, 19, 12, 4, 11, 15.

Step 1   Add all the numbers in the list: 5 + 7 + 19 + 12 + 4 + 11 + 15 = 73.

Step 2   Count how many numbers are in the list: There are seven numbers in the list.

Step 3   Divide the sum (the result of step 1) by the number of numbers (the result of step 2): 73 ÷ 7 = 10.4.

So, the mean is 10.4.

Example

Jason has four grades of equal weight in his history class. They are 82, 90, 88, and 85. What is Jason's mean (average) in history?

Add all the numbers in the list: 82 + 90 + 88 + 85 = 345.

Count how many numbers are in the list:

There are four numbers in the list.

Divide the sum (the result of step 1) by the number (the result of step 2): 345 ÷ 4 = 86.25.

The mean is 86.25.

### Finding the Median

The median is the middle number in a group of numbers arranged in sequential order. In a set of numbers, about half will be greater than the median and the same number will be less than the median.

Step 1   Put the numbers in sequential order.

Step 2   The middle number is the median.

Example

Find the median of the following set of numbers: 5, 7, 19, 12, 4, 11, 15.

Put the numbers in sequential order: 4, 5, 7, 11, 12, 15, 19.

The middle number is the median: The middle number is 11.

The median is 11.

In the last example, there was an odd number of numbers, so the middle number was easy to find. But what if you are given an even number of numbers? Let's see how it works.

Example

Find the median of the following set of numbers: 5, 7, 19, 12, 4, 11, 15, 13.

Put the numbers in sequential order: 4, 5, 7, 11, 12, 13, 15, 19.

The middle number is the median. But there are two middle numbers: 11 and 12. In this case, you find the mean (or average) of the two middle numbers. That value is your median. Remember, to find the mean of a set of numbers, you first add the numbers together (11 + 12 = 23). Then, you divide the sum by the number of numbers (23 ÷ 2 = 11.5).

The median is 11.5.

Why would you use the median instead of the mean? Let's say a teacher gives everyone above the class mean either an A or a B. Here are the grades on the most recent test.

The class mean is 71, so only six students will receive an A or a B on the test. All the other students will get a C or below. How would the result be different if the teacher used the class median to determine who gets an A and a B? In that case, everyone with a test score greater than 69 would receive either an A or a B on the test—that's eight students. About half the students would get an A or a B using the median.

Notice that the mean was raised by the one person who received a 110 on the test. Often, when one number changes the mean to be higher (or lower) than the center value, the median can be used instead.

### Finding the Mode

The mode refers to the number in a set of numbers that occurs most frequently. To find the mode, you just look for numbers that occur more than once and find the one that appears most often.

Examples
1. Find the mode of the following set of numbers: 5, 7, 9, 12, 9, 11, 15.
2. The number 9 occurs twice in the list, so 9 is the mode.

3. Find the mode of the following set of numbers: 5, 7, 19, 12, 4, 11, 15.
4. None of the numbers occurs more than once, so there is no mode.

5. Find the mode of the following set of numbers: 5, 7, 9, 12, 9, 11, 5.
6. The numbers 5 and 9 both occur twice in the list, so both 5 and 9 are modes. When a set of numbers had two modes, it is called bimodal.

As you can see, the mode isn't always a middle number in a set of numbers. Instead, mode shows clustering. Mode is often used in stores to decide which sizes, styles, or prices are most popular. It wouldn't make sense for a clothing store to stock up on the mean size or the median size of pants. It makes more sense to buy the sizes that most people wear. There's where the mode comes in.

Practice problems for these concepts can be found at:

Data Analysis, Statistics, and Probability Practice Problems: GED Math