Statistics Calculators ▶ Standard Deviation Calculator
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Our standard deviation calculator allows you to find the standard deviation, variance, mean, coefficient of variance, and margin of error for a data set. Provide your data set values and the tool will show the calculations needed.
“It is the square root of the variance of any statistical data set”
Our standard deviation calculator utilises the following formulas to calculate standard deviation:
\(σ = \sqrt{\dfrac{1}{N} \sum_{i=1}^N\left(x_{i} – μ\right)^2}\)
Where:
xi = Individual Value
μ = Average Mean Value
N = Total Number Of Values
\(s = \sqrt{\dfrac{1}{N – 1} \sum_{i=1}^N\left(x_{i} – \bar{x}\right)^2}\)
Where:
xi= Each Single Value In the Data Set
x = sample mean
N = total sample size
Let’s resolve an example to make your concept broader. Just stay focused!
How to find the standard deviation for the following raw sample data set below:
\( 3, 4, 9, 7, 2, 5 \)
Step 1(Calculate Mean Value):
\(\bar{x} = {\dfrac{3 + 4 + 9 + 7 + 2 + 5}{6}}\)
\(\bar{x} = {30}{6}\)
\(\bar{x} = 5\)
Step 2 (Calculate The Value Of \(\left(x_{i} – \bar{x}\right)\):
\(x_1-\bar{x} = 3 – 5 = -2\)
\(x_2-\bar{x} = 4 – 5 = -1\)
\(x_3-\bar{x} = 9 – 5 = 4\)
\(x_4-\bar{x} = 7 – 5 = 2\)
\(x_5-\bar{x} = 2 – 5 = -3\)
\(x_6-\bar{x} = 5 – 5 = 0\)
Now we have:
\((x_1-µ)^2 = (-2)^2 = 4\)
\((x_2-µ)^2 = (-1)^2 = 1\)
\((x_3-µ)^2 = (-4)^2 = 16\)
\((x_4-µ)^2 = (2)^2 = 4\)
\((x_5-µ)^2 = (-3)^2 = 9\)
\((x_6-µ)^2 = (0)^2 = 0\)
The variance and standard deviation calculator automatically determine all of these values without creating any difficulty for you.
Step 3 (Calculate Sample Standard Deviation):
Now we know that:
\(s = \sqrt{\dfrac{1}{N – 1} \sum_{i=1}^N\left(x_{i} – \bar{x}\right)^2}\)
\(s = \sqrt {\dfrac { 4+1+16+4+9+0}{ 6-1}}\)
\(s = \sqrt {\dfrac { 34 }{5}}\)
\(s = \sqrt {6.8}\)
\(s = 2.60\)
The simple interface of the STD calculator makes your calculations super fast and 100% accurate! What you need to do includes:
Inputs:
Outputs:
From the source of Wikipedia : General understanding and basic examples
From the site of scribbr.com : Formulas for population and sample standard deviation
Other Languages: Standart Sapma Hesaplama, Odchylenie Standardowe Kalkulator, Kalkulator Standar Deviasi, Standardabweichung Rechner, 標準偏差 計算, 표준편차 계산기, výpočet směrodatné odchylky, Calculadora De Desvio Padrão, Calculadora De Desviacion Estandar, Calcul Ecart Type, Calcolo Deviazione Standard Online, Калькулятор Среднеквадратичное Отклонение, حساب الانحراف المعياري, Keskihajonta Laskin.