# Statistics Calculator

Statistics calculator computes statistical values such as the mean, median, mode, variance, and standard deviation. Statistics is a branch of mathematics that deals with the analysis, collection, organization, representation, and interpretation of data.

## What is Statistics Calculator?

Statistics Calculator is an online tool that helps to calculate the mean, median, mode, variance, and standard deviation for the given numbers. Statistics is widely used in describing natural phenomena, and collecting appropriate quantitative data. To use this * statistics calculator*, 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 using an online statistics calculator:

**Step 1:**Go to Cuemath’s online statistics calculator**Step 2:**Enter the numbers separated by a comma in the given input box of the statistics calculator.**Step 3:**Click on the**"Calculate"**button to find the mean, median, mode, variance, and standard deviation.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How does Statistics Calculator Work?

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_{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 = [(n+1)/2]th Obs

If** **n is even, then use the formula:

Median = [n/2 Obs + [(n+1)/2]th Obs]/2

Mode for ungrouped data is found by selecting the most frequent item on the list.

Variance (σ^{2}) tells us how far a particular value is from the mean. In other words, it shows how a certain data point differs from the mean.

Variance(σ^{2}) = ∑(xr - μ )^{2} / n

where N is the number of observations, μ is the mean, and xr is the value in the observation.

Standard deviation is** **commonly denoted as SD, and it tells us about how much a particular value has deviated from the mean value. The square root of the variance gives the standard deviation.

Standard deviation = √(∑(xr - μ)^{2} / n)

## Solved Examples on Statistics

**Example 1:** Find the mean of 2, 8, 11, 25, 4, 7 and verify it using the statistics calculator

**Solution:**

The mean formula is given as (x1 + x2 + x3...+ xn) / 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} and verify it using the statistics calculator

**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} and verify it using the statistics calculator

**Solution:**

Since there is only one value repeating itself.

Therefore, Mode = {15}

Similarly, you can try the statistics 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
- 14, 16, 8, 14, 25

**☛ Math Calculators:**

visual curriculum