Calculating the mean, median, mode, and range of a data set is a fundamental part of learning statistics. Use this video to practice your skills and then test your knowledge with a short quiz.

Mean, Median, Mode & Range Definitions

The mean is the arithmetic average of a data set. This is found by adding the numbers in a data set and dividing by how many numbers there are. The median is the middle number in a data set when the numbers are listed in either ascending or descending order. The mode is the value that occurs the most often in a data set, and the range is the difference between the highest and lowest values in a data set.

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During this video, we will be looking at practice problems to help you find the mean, median, mode, and range of a data set. Since these are practice problems, feel free to pause the video during each example and try to work out the problems on your own. Then, play the video to check your answers.

Gasoline Prices

According to the U.S. Bureau of Labor Statistics, the gas prices for each month of the year in 2000 were as follows, rounded to the nearest hundredth of a decimal:

1.30, 1.37, 1.54, 1.51, 1.50, 1.62, 1.59, 1.51, 1.58, 1.56, 1.56, 1.49.

Let’s start with the mean. Pause the video here to see if you can find the mean of this data set. The mean of a data set tells us on average how much gas cost in the year 2000. We can find the mean by adding all of the numbers up and dividing by 12, which is the number of months in the year and how many numbers we have in this data set.

1.30 + 1.37 + 1.54 + 1.51 + 1.50 + 1.62 + 1.59 + 1.51 + 1.58 + 1.56 + 1.56 + 1.49 = 18.13 / 12 = 1.51

1.51 is the mean for this data set. This number tells us on average the price of gas for the entire year. You will notice that 1.51 appears in the data set. Sometimes you will have an average that does not appear in the data set, but will still show you the big picture of the numbers given.

Okay, let’s move on to median. Pause the video here to see if you can find the median of this data set. The median of a data set tells us what number falls directly in the middle. This is useful if you have one or two numbers that are greatly larger or smaller than the rest of the numbers in the data set. If the numbers are all pretty close together, then the mean and the median will be very close to the same number.

First, arrange the numbers in either ascending or descending order.

1.30, 1.37, 1.49, 1.50, 1.51, 1.51, 1.54, 1.56, 1.56, 1.58, 1.59, 1.62

Now, eliminate each number until you are down to the middle. I like to take one number from each end like this:


findingthemedian


So we are left with 1.51 and 1.54 with five numbers crossed out on each side. Sometimes you will have data sets that have an odd amount of numbers. When this happens you are left with one number as a median. In this case, we have two numbers because our data set has an even amount of numbers. When you are left with two numbers as the median, you need to find the average by adding the two numbers and dividing by 2.

1.51 + 1.54 = 3.05 / 2 = 1.53

I rounded this number to the nearest hundredth. The median is 1.53 and this tells us that exactly half of the data set is greater than 1.53 and exactly half of the data set is less than 1.53. Although it isn’t the same number, the mean and the median for this set of numbers is very close, meaning that the numbers in the data set are very close together.

Now let’s find the mode in this set of data. The mode is the number you will see the most in the data set. While mean and median give you a big picture idea, the mode gives you an idea of what number you are most likely to encounter. Let’s look at some numbers that repeat in the data set. I see two 1.51 numbers and two 1.56 numbers. In this data set, there are no other numbers that repeat. So in this case, we have two modes: 1.51 and 1.56.

Our last practice problem is finding range. You can find the range in the data set by taking the largest number and subtracting the smallest number. This will show you the spread in the numbers and how much difference there is between them. In this data set, our largest number is 1.62 and our smallest number is 1.30. Subtract those numbers.

1.62 – 1.30 = .32

This is our range. So now we know that over the course of the year 2000, the price in gas fluctuated a total of 32 cents.

Lesson Summary

Remember, the mean is the arithmetic average of a data set. You can find the mean by adding the numbers in a data set and dividing by how many numbers there are. The median is the middle number in a data set when the numbers are listed in either ascending or descending order, and the mode is the value that occurs the most often in a data set. The mode can tell you what numbers are most likely to come across in the data set. The range is the difference between the highest and lowest values in a data set. The range can tell you how much the data set fluctuates.

Learning Outcome

By the end of this lesson you should be able to explain and calculate the mean, median, mode, and range for a data set.