# Mean, Median, Mode: What's the difference? [With examples]

If you've ever scratched your head over the difference between mean, median, and mode, fret not – you're not alone.

While they may sound somewhat similar, they serve very different purposes. In other words, they aren't just tongue-twisting words, but essential tools that help us make sense of numbers in a snap.

In this article, we’ll be taking a closer look at how you can use each one of them to get the answers you are looking for.

## Overview

### Mean

Definition: The average of a data set

The mean, which is also called the 'average,' is found by adding up all the numbers in a group and then dividing that total by how many numbers there are. But be careful, if there are some really big or really small numbers, they can make the middle point move a bit away from where most of the other numbers are.

### Median

Definition: The most common number in a data set

The median is the number right in the middle when you put all the numbers in order from smallest to largest (or the other way around). Imagine you're lining up your friends by height, and the person in the middle is the median. This number can be a good guide, especially if there are some really tall or short folks who might mess up the average.

### Mode

Definition: The middle of a set of numbers

The mode is like the number that gets a prize for being repeated the most. If you're counting the colors of marbles and the red ones are the winners because there are more of them, red is the mode. It helps you find what's the most popular thing within your group.

## Tips to remembering the difference between Mean, Median, Mode

### The ‘Mean’ one: Mean

Out of the three, only Mean requires a formula. Since it’s the only one that needs you to add all the numbers together and divide them, you can remember it as the ‘Mean’ guy.

### The 'Middle' one: Median

Imagine arranging your numbers in order from smallest to largest. The median is the number right in the middle. It's like finding the buddy that splits the group in half. Even if a super big or super small number shows up, the median stays cool and centered.

### The 'Popular' one: Mode

Think of the mode as the superstar number – the one that appears the most. It's like the favorite ice cream flavor that everyone picks. If two or more numbers are tied, no worries – you can have more than one popular pick!

## Finding the Mean

Mean = Sum of all numbers / Total number of numbers

It's important to note that while there are many types of mean, more often than not, questions are referring to the arithmetic mean. Simply put, the arithmetic mean is the total sum of data divided by the number of data points.

Example

1,5,6,8,10,12 = 42

Step 2: Divide by no. of data points

42/6 = 7

The mean is 7.

## Finding the Median

Remember, the median is the middle value of the data in the middle position, when arranged in ascending order. To find the median, simply:

1. Arrange the data points in ascending order (smallest to largest)
2. If the total number of data points is even, simply take the average of the two middle data points. That's your median.
3. If the total number of data points is odd, the data point right in the middle is the median.

Example #1 [Odd data set]

8, 3, 5, 9, 1, 2, 7

Step 1: Arrange the data points in ascending order

1, 2, 3, 5, 7, 8, 9

Step 2: As there's an odd number of data points, locate the middle number to find the median.

The median is 5.

Example #2 [Even data set]

9, 3, 3, 8, 1, 2

Step 1: Arrange the data points in ascending order

1, 2, 3, 3, 8, 9

Step 2: As there's an even number of data points, find the median by getting the average of the middle two data points.

(3 + 3) / 2 = 3

The median is 3.

## Finding the Mode

Out of the three, finding the mode should be the easiest challenge. However, unlike mean and median, there can be more than one mode in a single data set. That's not all, you can also locate the mode of a non-numerical data set by following the same steps.

Example #1

In a class of 30 students, the exam scores are as follows:

85, 90, 75, 85, 80, 90, 85, 70, 75, 80, 85, 95, 90, 85, 70, 80, 75, 85, 90, 80, 85, 75, 80, 85, 75, 90, 85, 80, 85, 85

Step 1: Arrange the data points in order

70, 70, 75, 75, 75, 75, 80, 80, 80, 80, 80, 80, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 85, 90, 90, 90, 90, 90, 95

Step 2: Look out for the data point that occurs most often

85 (11 times)
80 (6 times)
90 (5 times)
75 (4 times)
70 (2 times)
95 (1 time)

The mode is 85.

Example #2

In a survey of 20 people, the following were the favorite ice cream flavors:

Chocolate, Vanilla, Strawberry, Chocolate, Mint, Chocolate, Strawberry, Chocolate, Chocolate, Vanilla, Strawberry, Mint, Chocolate, Vanilla, Chocolate, Strawberry, Mint, Mint, Strawberry, Chocolate

Step 1: Arrange the flavours in groups

Chocolate, Chocolate, Chocolate, Chocolate, Chocolate, Chocolate, Chocolate, Chocolate, Mint, Mint, Mint, Mint, Vanilla, Vanilla, Vanilla, Strawberry, Strawberry, Strawberry, Strawberry, Strawberry.

Step 2: Look out for the data point that occurs most often

Chocolate, Chocolate, Chocolate, Chocolate, Chocolate, Chocolate, Chocolate, Chocolate (7x)
Strawberry, Strawberry, Strawberry, Strawberry, Strawberry (5x)
Mint, Mint, Mint, Mint (4x)
Vanilla, Vanilla, Vanilla (3x)

The Mode is Chocolate.
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