Mean, Median, Mode, and RangeBROUGHT TO YOU BY POWERPOINTPROS.COM

Introduction Knowing how to find the mean, median, mode, and range of a set of data is very important. In this lesson, we’ll help you understand these concepts and how to find them.

Mean

What is the Mean of a set of data?The mean of a set of data is the same as the average of a set of data.

Finding the Mean of a Set of DataTo find the mean of a set of data, all you have to do is find the sum of the entire data set, and then divide by the number of numbers in the set.

Practice Finding the Mean of a Data SetLet’s say that we had to find the mean of this data set:

10, 11, 9, 12, 15, 13, 7, 8, 12

If we add all of these numbers together, we’ll have a sum of 97.

Practice Finding the Mean of a Data Set10, 11, 9, 12, 15, 13, 7, 8, 12If we add all of these numbers together, we’ll have a sum of 97.

To find the mean of this data set, we’ll have to take our sum, 97, divided by the number of numbers in the set, which is 9.After dividing 97, our sum, by the number of numbers, 9, we get the mean rounded to 10.78.

Things to Remember The mean of a set of data is the same as the average of a set of data. To find the mean of a data set, divide the sum of all of the numbers in the set by the number of numbers in the set.

Median

What is the Median of a set of data?The median of a set of data is the middle number in the set of data.

Finding the Median of a Set of DataTo find the median of a set of data, you must first arrange the set of data in numerical, or numbered, order. Then you should locate the middle number in the data set.

Practice Finding the Median of a Data SetLet’s say that we had to find the median of this data set:

10, 11, 9, 12, 15, 13, 7, 8, 12

If we are going to find the median, first, we must rearrange this set into numerical order.

Practice Finding the Median of a Data Set7, 8, 9, 10, 11, 12, 12, 13, 15Now that we’ve arranged this data set in numerical order, we can proceed to find the middle number.

We can keep crossing out a number from each side of this data set until we have our middle number.After crossing out numbers from each side of the data set, we can see that our median, or “middle number” is 11.

“Even” MediansThe process of finding the median went smoothly last time. After crossing out one number from each side 4 times, we were left with one number in the middle, and that remaining number was the median.

But what if we’re not left with 1 number in the middle?

“Even” MediansIn fact, this happens quite a bit. Any time you’re dealing with an even number of data points, you won’t have one number left in the middle when trying to find the median. You’ll be left with two!

Unfortunately, you can’t have 2 medians in a set of data. So then, what do we do?

“Even” Medians7, 8, 9, 10, 11, 12, 12, 13, 15, 16Let’s say that we were trying to find the median of this set of data.After crossing out 4 numbers from each side, we are now left with 2 numbers.We can’t cross out those 2 numbers or else there will be none left, but we can’t have 2 medians, so what do we do???

“Even” Medians7, 8, 9, 10, 11, 12, 12, 13, 15, 16In order to find the exact median of this data set, we have to find the number exactly in between 11 and 12. And we can do that using another trick we’ve just learned, finding the mean of 11 and 12!

“Even” Medians7, 8, 9, 10, 11, 12, 12, 13, 15, 16After finding the mean of 11 and 12, we can see that the median of this data set is 11.5, which is right in between our 2 remaining numbers, 11 and 12.

11.5

Things to Remember The median of a set of data is the middle number in a set of data. To find the median of a data set, you must first arrange the set of data in numerical order and then locate the middle number in that data set. If there are 2 middle numbers (in the case of data sets with an even amount of numbers), you must find the mean of those two numbers. That number is the median.

Mode

What is the Mode of a set of data?The mode of a set of data is the number (or numbers) occurring most often.

Finding the Mode of a Set of DataTo find the mode of a set of data, simply find the number(s) that occur most often. (It may help to arrange the set of data numerically.)

Practice Finding the Mode of a Data SetLet’s say that we had to find the mode of this data set:

10, 11, 9, 12, 15, 13, 7, 8, 12

It may help, especially at first, to arrange the data set in numerical order to better locate numbers occurring more than once.

Practice Finding the Mode of a Data Set7, 8, 9, 10, 11, 12, 12, 13, 15Now that we’ve arranged this data set in numerical order, look for any numbers occurring more than once first.

Since the number 12 is the only number occurring more than once, it is our mode.

More Information about Mode If no number occurs more than once in a data set, there is no mode. If there is more than one number occurring more than once, compare how often they each occur and only the one(s) that occur most often are modes. You can have more than one mode.

Things to Remember The mode of a set of data is most occurring number. To find the mode of a data set, look for number(s) that occur the most often. You may have no mode or multiple modes.

Range

What is the Range of a set of data?The range of a set of data is the difference between the lowest and highest numbers in a set of data.

Finding the Range of a Set of DataTo find the range of a set of data, find the highest and lowest numbers in that data set and subtract the lowest number from the highest number. (Once again, it may help to arrange the data set numerically for easier identification.)

Practice Finding the Range of a Data SetLet’s say that we had to find the range of this data set:

10, 11, 9, 12, 15, 13, 7, 8, 12

It may help, especially at first, to arrange the data set in numerical order to better locate the highest and lowest numbers.

Practice Finding the Range of a Data Set7, 8, 9, 10, 11, 12, 12, 13, 15Now that we’ve arranged this data set in numerical order, we can easily find the highest and lowest numbers.

The highest number is 15, and the lowest number is 7. After subtracting 7 from 15, we find our range of 8.

Things to Remember The range of a set of data is the difference between the highest and lowest numbers. To find the range of a data set, look for the highest and lowest numbers. Subtract the lowest number from the highest number.

Lesson Practice

Fill in the blanks with the correct answers.1. The _________ of a data set is the average,

found by finding the sum of all of the numbers and dividing it by the number of numbers in the set.

2. The ________ of a data set is the number(s) occurring most often.

mean

mode

Fill in the blanks with the correct answers.3. The _________ of a data set is the difference

between the highest and lowest numbers in the set.

4. The ________ of a data set is the middle number in that data set.

range

median

Find the mean, median, mode(s), and range of the following data sets.1. 1,5,2,4,3 Mean-

Median- Mode(s)- Range-

3 3

none 4

Find the mean, median, mode(s), and range of the following data sets.2. 6,8,7,12,10,11 Mean-

Median- Mode(s)- Range-

9 9

none 6

Find the mean, median, mode(s), and range of the following data sets.3. 20, 20, 18, 22, 21,

19 Mean- Median- Mode(s)- Range-

20 20

20 4

Find the mean, median, mode(s), and range of the following data sets.4. 12, 4, 8, 5, 1 Mean-

Median- Mode(s)- Range-

6 5

none 11

Find the mean, median, mode(s), and range of the following data sets.5. 6, 3, 6, 3, 2, 4, 8, 4 Mean-

Median- Mode(s)- Range-

4.5 4

6, 3, and 4 6

Conclusion Congratulations! You now know about mean, median, mode, and range and how to find them when given a data set!