Mean and Standard Deviation Calculator

'Mean and Standard Deviation Calculator' is an online tool that helps to calculate the mean and standard deviation for the given numbers. 

What is Mean and Standard Deviation Calculator?

Online Mean and Standard Deviation Calculator helps you to calculate the mean and standard deviation for the given numbers in a few seconds.

Mean and Standard Deviation Calculator

NOTE: Enter values inside the bracket, separated by a comma.

How to Use Mean and Standard Deviation Calculator?

Please follow the steps below to find the mean and standard deviation for the given numbers:

• Step 1: Enter the numbers separated by a comma in the given input box.
• Step 2: Click on the "Calculate" button to find the mean and standard deviation for the given numbers.
• Step 3: Click on the "Reset" button to clear the fields and find the mean and standard deviation for the different numbers.

How to Find Mean and Standard Deviation Calculator?

The mean or average of a given data is defined as the sum of all observations divided by the number of observations. The mean is calculated using the formula:

Mean or Average(x) = (x₁ + x₂ + x₃...+ x_n) / n , where n = total number of terms, x₁, x₂, x₃, . . . , x_n = Different n terms

Standard deviation is commonly denoted as SD, and it tells about the value that how much it has deviated from the mean value.

Standard deviation = √(∑(x_i - x)² / (N - 1)),

where x_i is individual values in the sample, and x is the mean or an average of the sample, N is the number of terms in the sample.

Solved Examples on Mean and Standard Deviation Calculator

Example 1:

Find the mean and standard deviation for the following set of data: {51,38,79,46,57}

Solution:

Given N = 5

Standard deviation = √(∑(x_i - x)² / (N - 1))

Mean(x) = 51 + 38 + 79 + 46 + 57 / 5 = 54.2

Standard deviation = √(51 − 54.2)² + (38 − 54.2)² + (79 − 54.2)² + (46 − 54.2)² + (57 − 54.2)² / (5 - 1)

= 15.5

Therefore, mean = 54.2, and standard deviation = 15.5

Example 2:

Find the mean and standard deviation for the following set of data: {1, 6, 7, 2, 9}

Solution:

Given N = 5

Standard deviation = √(∑(x_i - x)² / (N - 1))

Mean(x) = 1 + 6 + 7 + 2 + 9 / 5 = 5

Standard deviation = √(1 - 5)² + (6 - 5)² + (7 - 5)² + (2 - 5)² + (9 - 5)² / (5 - 1)

= 3.39

Therefore, mean = 5, and standard deviation = 3.39

Example 3:

Find the mean and standard deviation for the following set of data: {4, 8, 11, 19}

Solution:

Given N = 4

Standard deviation = √(∑(x_i - x)² / (N - 1))

Mean(x) = 4 + 8 + 11 + 19 / 4 = 42/4 = 10.5

Standard deviation = √(4 - 10.5)² + (8 - 10.5)² + (11 - 10.5)² + (19 - 10.5)² / (4 - 1)

= 6.35

Therefore, mean = 10.5, and standard deviation = 6.35

Similarly, you can try the calculator to find the mean and standard deviation for the following: 

a)  21,14,16,8,2,4,15,8

b)  25,1,7,15,6,14,14,25,7

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