## Introduction to Mean, Median & Mode

The most commonly used term is the average also known as finding where the middle of the data lies. There are three ways to measure the average: the mean, median, mode and sometimes also look for range.

Why these ways? Good question. Each will give you a different point of view at the numbers; depending on the question you're trying to answer **(or the argument you're trying to make)**, any of them could prove the most useful.

Mean, median, mode and range are numbers that represent a whole set of data or information. Mean, median, mode and range are together called the measures of central tendency. These are used to simplify comparisons of sets of numbers, especially large sets of numbers, by calculating the center values using mean, mode and median. Use the ranges and standard deviations of the sets to examine the variability of data in general mathematics and statistics.

## What is Mean?

The most common expression for the mean is that the dataset with a constant variable is the mathematical average of all the values included in the given dataset **(to calculate it use calculatored’s Mean Calculator)**, and add up all the values of dataset then divide it by the number of values. The mean of a distribution with a continuous variable, additionally referred to as the expectation, is obtained by integrating the product of the variable with its probability as defined by the distribution. The expected value is denoted by the minuscule Greek letter alphabetic character (µ).

## How to find Mean?

There are several types of mean in mathematics, but usually when people talk about mean, they are thinking about the arithmetic mean.

The arithmetic mean is the sum of all of the given values divided by the number of values.

$$\text{Mean}\;=\;\frac{\text{Sum of data}}{\text{Numbers Values}}$$

Here's the same formula written in mathematically form:

$$\text{Mean}\;=\;\frac{\sum X_i}{n}$$

Where, Xi are the values in the given dataset and n is the total number of values.

## What is Median?

The median of a distribution with a constant variable depends on whether or not the no. of terms within the distribution is even or odd. If the number of terms is odd, then the value of the term in middle is median value.

The median distribution with a continuous variable is the value m, specified to minimum probability which is of **1/2 (50%)**. It is specifically chosen on purpose to perform if the value is less than or equal to m. Its probability is minimum of **1/2** which is chosen to perform if the values are larger than or equal to m.

## How to find Median?

The median is the middle point in a set of given values, half of the values are smaller than the median and half of the values are larger and you can calculate it by.

**there are some rules to find the median:**

- Arrange the values from smallest to largest.
- If the number of given values is odd, the median is the middle value in the list.
- If the number of given values is even, the median is the average of the two middle values in the list.

## Example:

Find the median of this dataset:

111, 444, 222, 555, 000

Arrange the data in order first:

000, 111, 222, 444, 555

There is an odd number of values, so the median is the middle data points.

000, 111, 222, 444, 555

The median is 222.

## What is Mode?

The mode of a distribution with a constant variable is that the value of the term that occur the most typically. It's not uncommon for a distribution with a constant variable to have more than one mode, particularly if there aren't several terms. This happens if 2 or more of terms occur with equal frequency and more than any of the others.

A distribution with 2 modes is called bimodal. A distribution with 3 modes is named trimodal. The mode of a distribution with continuous variable is the maximum. Value like discrete distributions, there could also be more than one mode, here is the Mean Calculator introduced by calculatored.

## How to find Mode?

Sir John asked students in his class how many siblings they each had.

Find the mode of the dataset:

00, 00, 11, 11, 11, 11, 11,11, 22, 22, 22, 33, 55

Look for the value that occurs the most:

00, 00, 11, 11, 11, 11, 11, 11, 22, 22, 22, 33, 55

The mode is 11 siblings.

## What is Range?

The range of a distribution with a constant variable is that the difference between the maximum and minimum values. For a distribution with continuous variable, the range is the distinction between 2 extreme points on distribution curve, wherever the value of the function falls to zero. For any value outside the range of a distribution, the value of the function will be zero.

## How to find Range?

Sir Steve took 7 math tests in one marking period. What is the range of his test marks?

89, 73, 84, 91, 87, 77, 97

Arrange the test marks from least to greatest, we get:

73, 77, 84, 87, 89, 91, 97

Highest - Lowest = 97 - 73 = 24

The range of test marks is 24.

## What is a Mean Calculator?

Calculatored introduce Mean Calculator for calculation of mean, median, mode and range.

You have to enter values as shown in the figure above,

After you entered the values then press “CONVERT” button and the mean calculator will calculate mean, median, mode and range.