How to Find the Mean Mode and Median in Statistics

Probability and Statistics > Basic Statistics > How to find the mean mode and median

Stuck on how to find the mean mode median in statistics?

1. The mean is the average of a data set.
2. The mode is the most common number in a data set.
3. The median is the middle of the set of numbers.

Aren’t exactly sure what the difference is between the three? Watch the video or read Mean Mode Median below for a full explanation (and some tips to help you remember the differences between the three).

How to find the mean mode and median : Steps

How to find the mean mode and median: MODE

• Step 1: Put the numbers in order so that you can clearly see patterns.
For example, lets say we have 2, 19, 44, 44, 44, 51, 56, 78, 86, 99, 99. The mode is the number that appears the most often. In this case: 44, which appears three times.

How to find the mean mode and median: MEAN

• Step 2: Add the numbers up to get a total.
Example: 2 +19 + 44 + 44 +44 + 51 + 56 + 78 + 86 + 99 + 99 = 622.  Set this number aside for a moment.
• Step 3: Count the amount of numbers in the series.
In our example (2, 19, 44, 44, 44, 51, 56, 78, 86, 99, 99), we have 11 numbers.
• Step 4: Divide the number you found in step 2 by the number you found in step 3.
In our example: 622 / 11 = 56.5454545. This is the mean, sometimes called the average.
• Dividing the sum by the number of items to find the mean.

How to find the mean mode and median: MEDIAN

If you had an odd number in step 3, go to step 5. If you had an even number, go to step 6.

• Step 5: Find the number in the middle of the series.
This is the median. 2, 19, 44, 44, 44, 51,56, 78, 86, 99, 99.
• Step 6: Find the middle two numbers.
For example, 1, 2, 5, 6, 7, 8, 12, 15, 16, 17. The median is the number that comes in the middle of those middle two numbers (7 and 8), so that number would be 7.5 in this case. (To do this mathematically, add the two numbers together and divide by 2).

Tip:  You can have more than one mode. For example, the mode of 1, 1, 5, 5, 6, 6 is 1, 5, and 6.

Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds more step-by-step solutions, just like this one!

What is the Mean Mode Median? Definitions.

What is the Mean?

In statistics, the mean is the average of a set of data.
To find the mean, sum all the numbers and then divide by the number of items in the set. For example, to find the mean of the following set of numbers: 21, 23, 24, 26, 28, 29, 30, 31, 33
21 + 23 + 24 + 26 + 28 + 29 + 30 + 31 + 33 = 245
Then divide your answer by the number of items in your set. There are 9 numbers, so:
245 / 9 = 27.222

Dividing the sum by the number of items to find the mean.

Note: The word “mean” can have other interpretations outside of statistics. For example, when the weather service reports that a “mean daily temperature” is 75 degrees, that number was obtained by taking the sum of the high daily temperature and the low daily temperature and dividing by 2. This is what is called a “Midrange“. While this can be a cause of confusion, remember that in statistics, the mean is the average.

What is the Mode?

The mode is the most common number in a set. For example, the mode in this set of numbers is 21:
21, 21, 21, 23, 24, 26, 26, 28, 29, 30, 31, 33

What is the Median?

The median is the middle number in a data set. To find the median, list your data points in ascending order and then find the middle number. The middle number in this set is 28 as there are 4 numbers below it and 4 numbers above:
23, 24, 26, 26, 28, 29, 30, 31, 33

Note: If you have an even set of numbers, average the middle two to find the mean. For example, the mean of this set of numbers is 28.5 (28 + 29 / 2).
23, 24, 26, 26, 28, 29, 30, 31, 33, 34

Hint to remember the difference

Having trouble remembering the difference between the mean, mode and median? Here’s a couple of hints that can help.

• “A la mode” is a French word that means fashionable and it also refers to a popular way of serving ice cream. So “Mode” is the most popular or fashionable member of a set of numbers. The word MOde is also like MOst.
• The “Mean” requires you do arithmetic (adding all the numbers and dividing) so that’s the “mean” one.
• “Median” has the same number of letters as “Middle”.

If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you’re are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

How to Find the Mean Mode and Median in Statistics was last modified: June 20th, 2017 by
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30 thoughts on “How to Find the Mean Mode and Median in Statistics”

1. Lisa Barcomb

I found this article regarding the mode, mean, and median very helpful. It really makes me understand everything now in short and sweet steps. It really breaks everything down for you, so if you get stuck somewhere you know where you got caught up.

2. Evelyn Snyder

After reading the material in our textbook, this site really put it in perspective and made it easier to comprehend on how to find the mean, median and the mode.
To find the mean, median and/or mode depends if your set of numbers were even or odd. The step-by-step guide is very helpful.
Thanks

3. Hilary Dickert

Your easy step system is one that my mother showed me just recently! I’ve used it to determine my grades during mid-semester as well as my GPA at the end of a semester, before grades are posted. Having your guide makes this very easy and I’ve printed it out for referral purposes. Thanks!

4. Colin Tully

I found this information to be very helpful in understanding these concepts once again. I did all of this a long time ago in my early years of math, but i forget the main ideas over the years. Using a combination if the text book and other supplementary websites i really seem to understand the data a lot more!!! THANKS

5. Ashanti Jones

I think that this information is very helpful. It is definitely more helpful than the text I purchased for my STA course.

6. Lisa Barcomb

This part of the book is easy and helpful it allows you to find whatever you need to in a break down session so you will be able to understand how to do the problems that are involved in this subject.

7. crystal lydick

I found this blog really helpful to me. It is kinda funny because I never knew what any of these words meant until several weeks ago. My little boy is in 4th grade and in his homework, he had to tell what these words meant. I had no idea what they meant. I felt so bad, but we had to look them up. I wish I had already started statistics, because I would have know what to tell him. I really love how everything is broken down, makes it so much easier for me to understand.

8. Joni Poore

This site is amazing, I know mean, median and mode is basic but since this is the first step I looked at – I’m even more excited about possibly getting extra credit and getting things learned through a different perspective

9. Stephanie

4th grade is getting more challenging. I don’t remember learning mean and mode back in the day :)

I’m glad the site is helping though,
Stephanie

10. Nurse Jackie

Excellent site. Back to school to get my BSN. Never did statistics for ADN. This site makes it easy to understand.

11. saini

Its very easy to get understanding of mean. Mode and median ..iike this article as it was very helpful for me.

12. I'm from Salt Lake City, Utah

Wow. Very helpful. I highly recommend this. I have incredibly terrible math homework, but this helped me with it.

13. mobin

i think It is very helpful but i have small doubt suppose if there is no common number then what number we have to choose for mode – Ala mode ?