Statistics Calculator
Statistics is a branch of mathematics that deals with numbers and analysis of the data.
What is Statistics Calculator?
'Cuemath's Statistics Calculator' is an online tool that helps to calculate the mean, median, mode, variance, and standard deviation for the given numbers. This online Statistics Calculator helps you to calculate the mean, median, mode, variance, and standard deviation in a few seconds.
Note: Enter values inside the bracket, separated by a comma.
How to Use Statistics Calculator?
Please follow the steps below to find the mean, median, mode, variance, and standard deviation:
 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, median, mode, variance, and standard deviation.
 Step 3: Click on the "Reset" button to clear the fields and enter new values.
How to Find Statistics Calculator?
The mean or average of a given data is defined as the sum of all observations (obs.) divided by the number of observations. The mean is calculated using the formula:
Mean or Average = (x_{1} + x_{2} + x_{3}...+ x_{n}) / n , where n = total number of terms, x_{1},_{ }x_{2},_{ }x_{3}, . . . , x_{n} are different n terms
The median is defined as the value of the observation in the middle obtained after arranging the data in ascending order. To find the median of a given set of values.
If n is odd, then use the formula:
\(Median = \left(\frac{n+1}{2}\right)^{t h} \mathrm{obs.}\)
If n is even, then use the formula:
\(Median = \frac{\frac{n}{2} \text { obs. }+\left(\frac{n}{2}+1\right)^{t h} \text { obs. }}{2}\)
Mode for ungrouped data is found by selecting the most frequent item on the list.
Variance (σ^{2}) is the squared variation of values (X_{i}) of a random variable (X) from its mean (μ) for ungrouped data.
Variance(σ^{2}) = ∑(x_{i}  μ )^{2} / (N  1)
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))
Solved examples on Statistics Calculator

Example 1:
Find the mean of 2, 8, 11, 25, 4, 7
Solution:
The mean formula is given as (x_{1} + x_{2} + x_{3}...+ x_{n}) / n
= (2 + 8 + 11 + 25 + 4 + 7) / 6
= 57/6
= 9.5

Example 2:
Find the median for the dataset: {1,2,2,3,4,3,3}
Solution:
Arrange the data set in ascending order: {1,2,2,3,3,3,4}
Number of terms = 7, which is odd
Median = middle value i.e. 4th.
Since the fourth value in the data set is 3. Thus, median = 3
Therefore, the median of a given data set is 3.

Example 3:
Find the mode for the following set of data: {14,15,16,15,17,15,18}
Solution:
Since there is only one value repeating itself, it is a unimodal list.
Therefore, Mode = {15}
Similarly,
For a bimodal list: {85,86,88,88,91,90,86,92,95}, mode = {86,88}
For the data set: {7,7,8,8,8,9,10,12,12,14,15}, mode = {8}

Example 4:
Find the variance for the following set of data: {51,38,79,46,57}?
Solution:
Given N =5
For sample variance,
Sample variance(σ^{2}) = ∑(x_{i}  x)^{2} / (N  1)
Mean(μ) = 51 + 38 + 79 + 46 + 57 / 5 = 54.2
Variance = (51 − 54.2)^{2} + (38 − 54.2)^{2} + (79 − 54.2)^{2} + (46 − 54.2)^{2} + (57 − 54.2)^{2} / (5  1)
= 965.26 / 4
= 241.315

Example 5:
Find the 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
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Similarly, you can try the calculator to find the mean, median, mode, variance, and standard deviation for the following:
 21, 14, 16, 8, 2, 4, 15, 8
 25, 1, 7, 15, 6, 14, 14, 25, 7