Statistical Mean, Median and Mode Calculator

This Statistical Mean, Median and Mode Calculator takes a dataset of comma separated numbers and calculates the statistical mean, median and mode of the data set. This calculator also calculates the minimum value, maximum value, count of elements in the dataset and the sum of the numbers in the set.

Using Statistical Mean, Median and Mode Calculator

1. Enter the Data Set in comma separated format.
2. Press the Calculate button to get the result.

Arithmetic Mean

Arithmetic mean is the average of the collection of numbers (dataset). It is calculated by adding all the numbers in the collection and divided by the count of numbers in the collection. i.e. mean is the average of numbers in the dataset.

Formula

Let's call the collection of numbers { x₁, x₂, ... , x_n } as x. The arithmetic mean be x.

The formula to find arithmetic mean x is:

Example:

If x = { 1, 2, 3, 4, 5},

then n = 5.

So, mean x = ( x₁ + x₂ + ... + x_n ) / n = (1 + 2 + 3 + 4 + 5) / 5 = 3

Median

Median is the middle value of the given dataset of numbers arranged in an order form lower to higher value.

Formula

Consider a data set x = { x₁, x₂, ... , x_n }.

For odd number of elements:

If "n" is an odd number (i.e. the dataset has odd number of elements) then:

Example:

If x = { 1, 2, 3, 4, 5},

then n = 5.

So, Median of (x) = x_{(n + 1) / 2} = x_{(5 + 1) / 2} = x₃ (i.e. 3rd element) = 3

For even number of elements:

If "n" is an even number (i.e. the dataset has even number of elements) then:

Example:

If x = { 1, 2, 3, 4, 5, 6},

then n = 6.

So, Median of (x) = [x_{(n / 2)} + x_{(n / 2) + 1}] / 2 = (x₃ + x₄) / 2 = (3 + 4) / 2 = 3.5

Mode

In mathematical statistics, the value which appears most often in the given collection of numbers is called a mode of the data set. Based upon the number of modes, a data set can have one mode (unimodal) or multiple modes (bimodal, trimodal or multimodal).

Unimodal dataset

In the dataset {1, 2, 3, 4, 5, 4, 2, 2}, you can see that element 2 is repeated the most number of times. So the mode of this dataset is 2.

Bimodal dataset

In the dataset {1, 2, 3, 4, 5, 4, 2, 2, 4}, you can see the elements 2 and 4 are repeated the most number of times, three times each. So the modes of this dataset are 2, 4.

Multimodal dataset

In the dataset {1, 2, 3, 4, 5, 4, 2, 2, 4, 1, 1}, you can see the elements 1, 2 and 4 are repeated the most number of times, three times each. So the modes of this dataset are 1, 2, 4.

No mode dataset

In the dataset {1, 2, 3, 4, 5}, all the elements are equally spread. So, there is no mode in this dataset.

Minimum

The smallest value in the dataset is the minimum of the dataset.

Maximum

The largest value in the dataset is the maximum of the dataset.

Count

Count is the number of elements in the dataset.

Sum

The sum of the dataset is the total of all the elements in the dataset.

Formula

If the dataset is represented as { a₁, a₂, ... , a_n }, then, sum = a₁ + a₂ + ... + a_n.

Sum =

• C# program to calculate mean.
• C# program to calculate mean.
• C# program to calculate mode.
• More about arithmetic mean at wikipedia.