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# Statistics Calculator

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Statistics is a study of data analysis. This statistics calculator helps us to calculate the statistical information like minimum, maximum, count, mean, median, mode, standard deviation and variance. Plug in the set of data into the statistics calculator and get the appropriate values.

Below you can see other calculator's which are under statistics. These calculators will be helpful for future use.

## Steps

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Step 1 : Jot down the given set of data from the question. Using the formula below, determine the mean of the data set.
$\bar{x}$ = $\frac{x_1+x_2+x_3...+x_n}{n}$

Step 2 : Arrange the given observation in ascending order. Median is nothing but the center value that is in the middle of the given observation.

Step 3 : Mode is the number that repeats most often in the given observation.

Step 4 : Standard deviation and variance is calculated by the following formula,
Standard deviation, $\sigma$ = $\sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})^2}$

Variance = $\sigma^{2}$

## Problems

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Given below are some of the problems based on statistics.

### Solved Examples

Question 1: Determine the statistical information of the following data.
3, 5, 7, 4, 2
Solution:

Given observation : 3, 5, 7, 4, 2

Mean of the given observation,
$\bar{x}$ = $\frac{x_1+x_2+x_3...+x_n}{n}$

$\bar{x}$ = $\frac{3+5+7+4+2}{5}$

$\bar{x}$ = 4.2

Rearranging the given observation in ascending order,
2, 3, 4, 5, 7

Median = 4

Since no terms are repeated, no mode is present.

Standard deviation is given by,
$\sigma$ = $\sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})^2}$

$\sigma$ = $\sqrt{\frac{1}{5}{(3-4.2)^2+(5-4.2)^2+(7-4.2)^2+(4-4.2)^2+(2-4.2)^2}}$

$\sigma$ = $\sqrt{\frac{1}{5}{1.44+0.64+7.84+0.04+4.84}}$

$\sigma$ = 1.720

Variance = $\sigma^{2}$
Variance = $1.720^{2}$
Variance = 2.96

Question 2: Determine the statistical information of the following data.
7, 8, 15, 25, 7
Solution:

Given observation : 7, 8, 15, 25, 7

Mean of the given observation,
$\bar{x}$ = $\frac{x_1+x_2+x_3...+x_n}{n}$

$\bar{x}$ = $\frac{7 + 8 + 15 + 25 + 7}{5}$

$\bar{x}$ = 12.4

Rearranging the given observation in ascending order,
7, 7, 8, 15, 25

Median = 8

As 7 is repeating two times, 7 is the mode.

Standard deviation is given by,
$\sigma$ = $\sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})^2}$

$\sigma$ = $\sqrt{\frac{1}{5}{(7-12.4)^2+(8-12.4)^2+(15-12.4)^2+(25-12.4)^2+(7-12.4)^2}}$

$\sigma$ = $\sqrt{\frac{1}{5}{29.16+19.36+6.76+158.76+29.16}}$

$\sigma$ = 6.974

Variance = $\sigma^{2}$
Variance = $6.974^{2}$
Variance = 48.64