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Statistics Calculator
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Statistics calculator is an important online statical calculator which helps to do the fundamental calculation in an easy manner. Statistics calculator is a simple calculator and its a great tool for the students. Fundamental measurements means the calculator for mean, median, mode, standard deviation,variance etc. The equation for each measure is given in the following section.

## Steps for Statistics Calculator

Step 1 :

Write down the observations from the question.

Step 2 :

Determine the mean using the given formula.
$\bar{x}$=$\frac{x_{1}+x_{2}+x_{3}+.....+x_{n}}{n}$

Step 3 :

Median is the middle value, when the observation is arranged some numeric order.

Step 4 :

Mode is the repeated number in given observation.

Step 5 :

Calculate the standard deviation and variance using the equation.

Standard deviation, $\sigma$ =$\sqrt{\frac{1}{n}\sum_{i=0}^{n}(x_{i}-\bar{x})^{2}}$

Variance=$\sigma ^{2}$

## Problems on Statistics Calculator

1. ### Calculate the fundamental statistical measurements of the following data.11,18,14,8

Step 1 :

Given observation is

11,18,14,8

Step 2 :

Mean is given by,

$\bar{x}$=$\frac{x_{1}+x_{2}+x_{3}+.....+x_{n}}{n}$

$\bar{x}$=$\frac{11+18+14+8}{4}$=12.75

Step 3 :

Rearranging the given observation,

8,11,14,18

Median is given as 12.5

Step 4 :

Since there is no repeated terms, no mode value is present.

Step 5 :

Standard deviation is given by the equation,

$\sigma$ =$\sqrt{\frac{1}{n}\sum_{i=0}^{n}(x_{i}-\bar{x})^{2}}$

$\sum_{i=0}^{n}(x_{i}-\bar{x})^{2}$=(8-12.75)2+(11-12.75)2+(14-12.75)2+(18-12.75)2=54.75

$\sigma$ =$\sqrt{\frac{1}{4}×54.75}$=3.6996

Variance=$\sigma ^{2}$=$3.6996 ^{2}$=13.6875

Mean=12.75

Median=12.5

No mode

Standard deviation, $\sigma$ =3.6996

Variance=13.6875

2. ### Find out the fundamental statistical measure of the following observation.14,8,6,13,6

Step 1 :

Given observation is,

14,8,6,13,6

Step 2 :

Mean is given by,

$\bar{x}$=$\frac{x_{1}+x_{2}+x_{3}+.....+x_{n}}{n}$

$\bar{x}$=$\frac{14+8+6+13+6}{5}$=9.4

Step 3 :

Rearranging the given observation,

6,6,8,13,14

Median is given as 8

Step 4 :

Repeating terms gives the mode value.

So, mode=6

Step 5 :

Standard deviation is given by the equation,

$\sigma$ =$\sqrt{\frac{1}{n}\sum_{i=0}^{n}(x_{i}-\bar{x})^{2}}$

$\sum_{i=0}^{n}(x_{i}-\bar{x})^{2}$=(6-9.4)2+(6-9.4)2+(8-9.4)2+(13-9.4)2+(14-9.4)2=59.2

$\sigma$ =$\sqrt{\frac{1}{5} \times 59.2 }$=3.4409

Variance=$\sigma^{2}$=$3.4409^{2}$=11.84

Mean=9.4

Median=8

Mode=6

Standard deviation, $\sigma$ =3.4409

Variance=11.84

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