How to Find the Mean, Median, Mode and Range

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Statistics is extremely useful not only in getting good scores in your GED exam but in your daily life as well.

If someone asks you for example, how many text messages you send daily, you don’t have to recount every text from each week. You would use an average, and that is statistics.

In this lesson, you will learn some of the most basic concepts in statistics for GED: mean, median, mode and range. While these terms may sound technical, they are actually very simple concepts.

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What is Central Tendency

Often in life, we are presented with various sets of data. Each set may contain several pieces of information, usually in number form. Take for example this set of numbers.

(1, 2, 5, 7, 6, 4, 8)

This set of numbers could mean anything from different ages of children to the number of chocolate bars you ate last week. Let us say for example that the above number set represents the different heights of the plants in your garden by inches.

When somebody asks you how tall your plants are, do you need to recount to them each and every height of your plants? No, you just need one number. You need to find the number or data that represents all the data. That is called the central tendency. You can, for example, tell them the average height of all the plants or the median height or the mode.

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How to Find the Mean?

Mean is known more by its other name: average. This is the most commonly used measure of central tendency. In schools, for example, grades are averaged in order to measure how well a student’s performance is in all subjects combined. An average is used to represent a set of data using only a single number. For example, we can get:

– Average height – Average temperature – Average grade – Average weight

To find an average, you simply add all the number of the set and divide the sum by the number of data in the set. For the number set above, for example, you need to add each number.

1+2+5+7+6+4+8=33

Then divide 33 by 7, the number of values, to get an average of about 4.7 (33 ÷ 7 = 4.71).

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How to Find the Median

Don’t be alarmed by the technical term, median simply means middle value. That means if the number set is arranged from the lowest to the highest value or vice versa, the middle number is the median. Take for example the following number set:

(40, 60, 76, 89, 90, 101, 1000)

The number 89 is the median. However, if the numbers are not ordered from lowest to highest like for example:

(40, 60, 1000, 89, 90, 76, 101)

You have to arrange the numbers from the lowest to the highest value, then find the middle number. But if you have an even number set, like the one below, you need to arrange the numbers from lowest to the highest and find the two middle numbers, then find the average of those two numbers.

(200, 400, 606, 402, 306, 222) Needs to be arranged

(200, 222, 306, 400, 402, 606) Already arranged from lowest to the highest value

(200, 222, 306, 400, 402, 606) The two middle numbers are 306 and 400.

306+400=706, and 706 divided by 2 = 353, so the median is 353.

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How to Find the Mode

The mode is simply the most common number in a data set. All you have to do to find the mode is to look for the number that appears most in the set. Take for instance the number set below.

(1, 3, 4, 3, 5, 3, 7, 8, 9, 3, 4, 6, 7, 4, 3)

In this number set, the mode is the number 3. However, if you are not careful, you may get confused by the other repeated numbers which makes it a good idea to arrange the set from the lowest to the highest value first:

(1, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 7, 7, 8, 9)

Now that is less confusing. Make it a habit to arrange the numbers in a set from the lowest to the highest value first when looking for the mode.

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How to find the Range

In a number set, the range is simply the difference in value between the largest and the smallest number. To find the range, subtract the smallest value from the largest value. For example, look at the set of numbers below:

(105, 200, 600, 400, 6000, 750)

The smallest number in the set above is 105 while the biggest number is 6000. If you subtract 105 from 6000, you get 5895, which is the range.

As you can see, if you strip these statistic terms of their technical sounding names, they are very easy and less scary. As with all things that involve numbers, you have to be careful so that you won’t make mistakes. It takes practice and patience, but if you familiarize yourself with numbers, your math exams, including your GED test, will be easy.

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Related Topics

Sources

2.5 Measures of the Center of the Data, OpenStax Introductory Statistics 2e