### Mean, Median, Mode and Range Calculator

In mathematics, we have to come across a large set of data. To get valuable information about this large set of data, we get help from measures of central tendency. The measures of central tendency provide us with statistical information about this set of information. Mean, median, mode and range are known as four primary measures of central tendency. These four measures of information provide us with individual information about the set of data. After combining this information, we can easily know how these data points are connected. The brief explanation about the mean, median, mode and range are given below;

# What Is Mean?

Mean is also known as the average value of the given set of data. If you have a discrete set of numbers, its central value is known as mean. Mean is denoted by ‘X̄’. If you have X1, X2, ..., Xn numbers, mathematical formula to find mean of the data is given below;
X̄ = X1+X2+…+Xn/n
X̄ = ΣX/n

# Steps to Calculate the Mean

To calculate the mean of a discrete set of numbers, you will have to follow the following steps;
Ø  First of all, you should determine the numbers of the set. These numbers should consist of the real numbers only. It means that these numbers should not be variables. You should also try to arrange these numbers in the ascending order.
Ø  Secondly, you should add these numbers to find the sum. For this reason, you can use a calculator or you can also add these numbers by hand.
Ø  Thirdly, you should count all the values. If a specific value is repeated in your set, you should count each value to get the total.
Ø  At last, you will have to divide the sum of the values on the total number of values. In this way, you will get mean of the set of discrete numbers.
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Difference Between Rational And Irrational Numbers

# Types of Mean

Mean is known as the most commonly used central tendency measure. Mean is further divided into three types. These three types of the mean are explained below;

## Ø  Arithmetic Mean

The arithmetic mean is simply known as the average of the data because we can easily obtain the arithmetic mean by dividing the sum of the values over the total number of the values. The arithmetic mean is denoted by ‘X̄’. The formula to calculate the arithmetic mean is given below;
X̄ = X1+X2+…+Xn/n
X̄ = ΣX/n

## Ø  Example of Arithmetic Mean

Find the arithmetic mean of the data 4, 10, 22 and 32.
A.M = 4+10+22+32/4
A.M = 68/4
A.M = 17

## Ø  Weighted Arithmetic Mean

If we have such data in which values don’t have equal importance, we have to provide certain numerical values to provide them with relative importance. These numerical values are known as weights. If X1, X2, ……, Xn have values and their weights are W1, W2,….., Wn. We can find the weighted mean by using the following formula;
w = W1X1+ W2X2+…+ WnXn/ΣW
w = ΣWX/ ΣW

## Ø  Example of Weighted Mean

If a student obtains marks 78, 98 and 96 out of 100 from English, Physics and Chemistry and weights for these subjects are 2, 3 and 4 respectively, find its weighted mean.
w = 78x2+98x3+96x4/9
w = 156+294+384/9
w = 834/9
w = 92.67

## Ø  Geometric Mean

Geometric Mean is denoted by ‘G’. If we want to find the geometric mean of a set of n positive values X1, X2, ……, Xn, first of all, we have to find their product. After that, we have to take the nth root of their product. The formula to find Geometric Mean is given below;

## Ø  Example of Geometric Mean

Find geometric mean of the set of the numbers 1,3 and 9.

## Ø  Harmonic Mean

Harmonic Mean is denoted by ‘H’. To find the harmonic mean of a set of n positive values X1, X2, ……, Xn, we have to find the reciprocal mean of the reciprocal of the values. The formula to find harmonic mean is given below;

## Ø  Example of Harmonic Mean

Find the harmonic mean of the values 7, 9, 11 and 12.

# What is the Median?

The median is a value in the data set which separates the higher half from the lower half. Therefore, the middle value in a data set is known as the median. The most important benefit of the median is that it provides us with a better idea about the typical value. For example, if you want to get an idea about household income, you can get its value in two ways. First, you can find it by mean but the problem with the mean is that it can either provide you with the lowest value or the highest value. The second way is to find it by the median. As median provides us middle value, therefore, it is the best way to find the typical value of a data set.

# Steps to Find Median

Based on the total numbers of values in a data set, we use two formulas to find the median of the data set.

## Ø  Finding the Median of the Odd Values

To find the median of the odd values, you should follow the following steps;
Ø  You should arrange the values in the ascending order.
Ø  You should separate the half values from the left side and half values from the right side. For example, if you have 7 values, you should separate three values from the left side and three values from the right side.
Ø  The middle value will be the median of the data set.

## Ø  Example to Find Median of the Odd Values

Find the median of the data set 2, 3, 9, 7, 0, 6 and 5.
First of all, we should arrange the values in the ascending order.
0, 2, 3, 5, 6, 7, 9.
As the total number of values is 7. Therefore, we should separate three values from the right side and three values from the left side.
0, 2, 3, 5, 6, 7, 9.
As ‘5’ is the middle value. Therefore, ‘5’ is the median of the data set.

## Ø  Finding the Median of the Even Values

To find the median of the even numbers, you should follow the following steps;
Ø  Like the odd values, you should arrange the values in the ascending order.
Ø  You should separate the half values from the left side and half values from the right side by leaving two values in the middle.
Ø  By taking the mean of the two middle values, we can get the median of the data set.

## Ø  Example to Find Median of the Even Values

Find the median of the data set 2, 7, 8, 9, 5, 0, 7 and 3.
By arranging the values in the ascending order.
0, 2, 3, 5, 7, 7, 8, 9.
As there are eight values in this data set, therefore, we should separate three values from the right side and three values from the left side.
0, 2, 3, 5, 7, 7, 8, 9.
As 5 and 7 are in the middle. So, by taking mean of these two values, we get ‘6’. Therefore, ‘6’ is the median of this data set.

# What is Mode?

In a data set, the value that appears more often is known as a mode. Like mean and median, the mode is also an essential way to express some specific information about a data set.
Rules to Find Mode of a Data Set
Like mean and median, there are also some rules to find the mode of the data. These rules are explained below;
Ø  First of all, you should arrange the values in a data set in the ascending order.
Ø  If one value is appearing more often in the data set, this value is known as the mode of the data set.
Ø  If more than one values are appearing more often in the data set, these values are known as the mode of the data set. It means that a data set can also have more than one mode.
Ø  If no value is repeating in the data set, this data set doesn’t have a mode.

# Examples to Find Mode of the Data Set

## Ø  Example 1

Find Mode of the data set 2, 3, 4, 2, 6, 7, 8, 2 and 0.
0, 2, 2, 2, 3, 4, 6, 7, 8.
As ‘2’ is repeated more often three times, therefore, ‘2’ is the mode of this data set.

## Ø  Example 2

Find Mode of the Data Set 2, 3, 4, 2, 3, 8, 9, 0 and 6.
0, 2, 2, 3, 3, 4, 6, 8, 9.
As ‘2’ and ‘3’ are repeated for two times, therefore’ ‘2’ and ‘3’ are the modes of the data set.

## Ø  Example 3

Find Mode of the Data Set 1, 42, 26, 39, 10, 5, 6, 7 and 8.
1, 2, 5, 7, 8, 10, 26, 39, 42.
As no value is repeated for more than one time, therefore, there is no mode of this data set.

# What is Range?

The difference between the largest and the smallest values in a data set is known as its range. The range of a data set provides us with specific value about the data set because we have to subtract the smallest value from the largest value.

## Steps to Find Range of a Data Set

To find out the range of a data set, you should follow the following steps;
Ø  First of all, you should arrange the values of the data set in the ascending order.
Ø  Secondly, you should mark the smallest value in the data set.
Ø  Thirdly, you should make the largest value in the data set.
Ø  At last, you should subtract the smallest value from the largest value.
Ø  The result of this subtraction is known as the range of the data set.

## Example to Find Range of the Data Set

Find the range of the data set 32, 22, 38, 40, 50 and 12.
12, 22, 32, 38, 40, 50.
Smallest value = 12
Largest value = 50
Range = Largest value – The smallest value
Range = 50 – 12

# Example to Find Mean, Median, Mode and Range of the Data Set

Find Mean, Median, Mode and Range of the data set 3, 8, 9, 5, 12, 15, 6, 0, 3.
The ascending form of the data set is given below;
0, 3, 3, 5, 6, 8, 9, 12, 15.

## Mean

X̄ = ΣX/n
X̄ = 0+3+3+5+6+8+9+12+15/9
X̄ = 61/9
X̄ = 6.78

## Median

0, 3, 3, 5, 6, 8, 9, 12, 15.
Median = 6

## Mode

0, 3, 3, 5, 6, 8, 9, 12, 15.
As ‘3’ is repeated more often, therefore, ‘3’ is known as the median of the data set.
Mode = 3

## Range

Smallest value = 0
Largest value = 15
Range = 15 – 0
Range = 15.
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