Contents:

- Overview and Definitions
- How to find the mean, median and mode by hand.
- Find the mean, median and mode with Technology:

## Overview

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

- The mean is the average of a data set.
- The mode is the most common number in a data set.
- 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 the mean, median and mode definitions below for a full explanation (and some tips to help you remember the differences between the three).

## What are the mean, median and mode? 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

First **add them all together**:

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

**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, median and mode? 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”.

## How to find the mean, median and mode by hand: Steps

### How to find the mean, median and mode: 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, median and mode: 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**.

### How to find the mean, median and mode: 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!

## SPSS Mean mode median

In order to find the SPSS mean mode median, you’ll need to use the **Frequency tab**. It seems a little counter-intuitive, but the Descriptive Statistics tab does not give you the option to find the mode or the median.

SPSS has a very similar interface to Microsoft Excel. Therefore, if you’ve used Microsoft Excel before, you will quickly adapt to SPSS.

## SPSS Mean Mode Median: Steps

Watch the video or read the steps below:

**Sample question:** Find the SPSS mean mode median for the following data set: 20,23,35,66,55,66

Step 1: **Open SPSS.** In the “What would you like to do?” dialog box, click the “type in data” radio button and then click “OK.” A new worksheet will open. Note: If you have opted out of the first help screen, you may not see this option. In that case, just start at Step 2.

Step 2: **Type your data into the worksheet.** You can type the data into one column or multiple columns if you have multiple data sets. For this example, type 20, 23, 35, 66, 55, 66 into column 1. Do not leave spaces between the data (i.e. don’t leave any empty rows).

Step 2: **Click “Analyze,” hover over “Descriptive Statistics” and then click “Frequencies.”**

Step 3: **Click “Statistics” and then check the boxes “mean”, “mode” and “median.”** Click “Continue” twice (select “none” as the chart type in the second window).

**Note**: In some versions of SPSS, you may only have to click “Continue” once and it may not give you an option for chart type.

The frequency results will appear as output. The top part of the output will display the mean, mode and median.

If you scroll down, the frequency table will also show you the mode. The mode is defined in statistics as the number with the highest frequency (for this sample data set, the number appearing the most is 66, with two results in the frequency column).

## Mean Median Mode TI 89

This article and short video explains how to use your calculator to enter a list of data and quickly find the

**mean, median, and mode on the TI 89**. The mean is the average of a data set, the median is the “middle” of the data set (the number that would fall in the middle if you were to write the numbers in order) and the mode is the number that appears most often.

## Mean Median Mode TI 89 Steps

Watch the video or read the steps below:

**Sample problem**: Find the mean, mode, and median for the following list of numbers: 1, 9, 2, 3, 7, 8, 9, 2.

**Step 1:** Press APPS then scroll to Stats/List Editor (scroll with the arrow keys at the top right of the keypad). Press ENTER.

If you don’t see the Stats/List editor, you need to download it. Follow the instructions here.

**Step 2:** *Clear any data in the list editor by pressing F1 then 8.*

**Step 3:** * Press ALPHA 5 ENTER. *This names your list “m.” Make sure m appears in the field: if 5 appears, it means the Alpha key didn’t work: try it again. Note: you can name the list anything you like.

**Step 4:** *Enter your numbers, one at a time. *Follow each entry by pressing the ENTER key. For our group of numbers, enter

1 ENTER

9 ENTER

2 ENTER

3 ENTER

7 ENTER

8 ENTER

9 ENTER

2 ENTER

**Step 5:*** Press F4, then* ENTER (for the 1-var stats screen).

**Step 6:** *Tell the calculator you want stats for the list called “m” by entering * ALPHA 5 into the “List:” box. The calculator should automatically put the cursor there for you. Press ENTER ENTER.

**Step 7:** *Read the results for the mean.* The mean is the first in the list (an x with a bar on top),= **5.125**.

**Step 8:*** Read the results for the median:*The median is about half way down the list: scroll with the down arrow and look for MedX = **5**.

**Step 9:*** Find the mode:* Return to the list editor. Press F3 2 ENTER ENTER to access “sort list”. Make sure “m” is in the “List:” box and the order is “Ascending.” Press ENTER. Your data is now sorted. Just count which number appears the most: that’s your mode.

**Tip**: You can name your list anything you want, but keep it simple and don’t use common variables like t,x,y, or z.

That’s it!

Lost your guidebook? You can download a new one from the TI website here.

## TI 83 Mean, Median, and Mode

Finding the **TI 83 mean** or **TI 83 median** from a list of data can be accomplished in two ways: by entering a list of data, or by using the home screen to type the commands. Using the list feature is just as easy as entering the data onto the home screen, and it has the added advantage that you can use the data for other purposes after you have **calculated your mean, mode and median** (for example, you might want to create a TI 83 histogram).

## Steps for the Mean, Median and Mode on the TI 83

Watch the video for the mean and median or read the steps underneath (for the mode, see this note):

**Example problem**: Find the mean and the median for the height of the top 20 buildings in NYC. the heights, (in feet) are: 1250, 1200, 1046, 1046, 952, 927, 915, 861, 850, 814, 813, 809, 808, 806, 792, 778, 757, 755, 752, and 750.

**Step 1:** Enter the above data into a list. Press the STAT button and then press ENTER. Enter the first number (1250), and then press ENTER. Continue entering numbers, pressing the ENTER button after each entry.

**Step 2:** Press the STAT button.

**Step 3:** Press the right arrow button to highlight “Calc.”

**Step 4:** Press ENTER to choose “1-Var Stats” and then type in the list name. For example, to enter L1 press [2nd] and [1].

**Step 5:** Press ENTER again. The calculator will return the mean, x̄. For this list of data, the TI 83 mean is **884.05** feet (rounded to 3 decimal places).

**Step 6:** Arrow down until you see “Med.” This is the TI 83 median; for the above data, the median is **813.05** feet.

Note: The TI-83 plus doesn’t have a built in mode function, but once you’ve entered your list, it’s pretty easy to spot the mode: it’s just the number that occurs most often in the set. Not sure? Read more about the mode here.

That’s it!

Lost your guidebook? Download a new one here at the TI website.

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*.

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