# Mean, Median, Mode, Standard Deviation Calculator Tanvesh
Masters in Structural Engineering | Research Interest - Artificial Intelligence and Machine learning in Civil Engineering | Youtuber | Teacher | Currently working as Research Scholar at NIT Goa

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Statistical analysis calculator to find mean, median, mode, standard deviation based on population and sample, geometrical mean, harmonic mean, quartiles.

## How to use Calculator

This statistical calculator is programmed to find the mean, median and mode standard deviation and quartiles for a one dimensional range of data.

1. Enter the numbers separated by comma or separated by space or vertically stacked data copied from excel.
2. 3. User can input whole number (eg: 2,3 etc.) or decimal numbers (eg: 3.5, 9.2 etc.), but care should be taken that fraction should not be put (eg: 3/7, 2/3 etc.)

## Mean Calculator

There are mainly 3 types of means namely:

1. Arithmetic mean
2. Geometric mean
3. Harmonic mean

Arithmetic mean: What is arithmetic mean? It is the average of all numbers present in a range of data, mean can be found for a one dimensional range, and for two dimensional range we can find the weighted average.

How to calculate mean, let us say we have ‘N’ numbers ranging from x1,x2,x3,x4,…… xn, then the mean is given as :

AM=\frac{x_{1}+x_{2}+x_{3}+\cdots+x_{n}}{N}

Geometric Mean: The geometric mean calculator calculates the geometric mean for a range of data specified by the user.

What is a geometric mean? It is a special type of mean which is calculated by taking the product ‘n’ values in a data range and then ‘n’th root of the product. The formula for geometric mean is given as:

GM=\sqrt[n]{x_{1} * x_{2} * x_{3} * \cdots * x_{n}}

Harmonic mean: The harmonic mean is given as ratio of number of values in a data range ‘n’ to the summation of inverse of all values in a data range. The harmonic mean is given by following formula:

H M=\frac{n}{\sum_{i=1}^{n}\left(\frac{1}{x_{i}}\right)}

## Median Calculator

This statistical calculator is programmed to find the median of the given range of one dimensional data. In simple words median is the middle value of a data range when arranged in ascending order.

When the data is arranged in an ascending order then for a data with even number of values, median is the average between (n/2) th value and (n/2 + 1) th value.

If the data range has odd number of values then the median is given as (n+1)/2 th value.

## Standard Deviation calculator

Standard deviation is the quantity that describes how much the entire data varies from the mean of the data.

Formula for standard deviation for population:

\sigma_{p}=\sqrt{\frac{\sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2}}{n}}

Formula for standard deviation for sample:

\sigma_{s}=\sqrt{\frac{\sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2}}{n-1}}

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