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Variance and Standard Deviation

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Standard Deviation is the part of statistics that defines the diversity of the value in the data set of value. It is widely used to find out the variability of the values from its mean value. We can say standard deviation defines the variation from the mean value or defines the dispersion from average value. Standard deviation helps to find the central tendency of the values that means if the value of the standard deviation is less means it is near to the mean value or if value is greater that means it is far from the mean or average value. Standard deviation is denoted by the symbol called as sigma ( s ) and it is used for measure of spread .Some times when talk about the standard deviation it is denoted as the square root of the variance that is define as the s2. For defining the standard deviation we have some value for the given distribution. For random variable ‘x’ mean value is defined as ‘m’ it is denoted by E | x | = m. Where ‘E’ denotes the average value of ‘x’ and formula for standard deviation is (s) = √ E (x - m )2,
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Variance and Standard Deviation
Variance and Standard Deviation
Standard Deviation is the part of statistics that defines the diversity of the value in the data set
of value. It is widely used to find out the variability of the values from its mean value. We can
say standard deviation defines the variation from the mean value or defines the dispersion
from average value.
Standard deviation helps to find the central tendency of the values that means if the value of
the standard deviation is less means it is near to the mean value or if value is greater that
means it is far from the mean or average value.
Standard deviation is denoted by the symbol called as sigma ( s ) and it is used for measure
of spread .Some times when talk about the standard deviation it is denoted as the square root
of the variance that is define as the s2.
For defining the standard deviation we have some value for the given distribution.
For random variable `x' mean value is defined as `m' it is denoted by E | x | = m.
Where `E' denotes the average value of `x' and formula for standard deviation is (s) = E (x -
m )2,
Know More About :- Bernoulli Effect

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Standard deviation is defined by the square root of the variance of `x'. When we talk about the
variance that is defined as the square of the standard deviation as s2that defines the measure
of farness of the value from the mean value in the given data set.
It is also described in terms of calculation first of al in the data set subtract the mean value
from each value.
That is defined by the difference between the mean value and data set value that is defined as
distance then square every distance value and then add these values. After adding al the
squared values divide this sum by the number of values in the data set.
We take an example to understand the standard deviation and variance,
Given below is the dataset,
Variable: a1, a2, a3, a4, a5, a6.
Value: 3, 4, 4, 5, 6, 8.
Then find the Variance and Standard Deviation for the values of given data set?
Solution: First of al find the average for the values of data set as a 6i = 1 a i.
That is defined as a1 + a2 + a3 + a4 + a5 + a6 = 3 + 4 + 4 + 5 + 6 + 8 = 30,
Finding the mean for this as m = a 6i= 1ai / n = 30 / 6 = 5,
After finding the value of mean find the variance as s2 = a (x - m) 2/ n.
The above equation can be simplified as s2= a x 2 / n - m2.

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Now by using above formula we can calculate the value of variance s2that is equal to 2.67
and the standard deviation that is the square root of the variance denoted as sis equals to
1.63.
Finding Variance and Standard Deviation
The Steps involved in calculating Variance and standard deviation are as follows:
First, Calculate the average (mean) of the data
Subtract the average value from the actual value for each period. This gives us the deviation
for both periods.
Square each period's deviation.
Sum the squared deviations.
Divide the sum of the squared deviations by the quantity of periods. This gives the variance
Taking square root of the variance, we get the standard deviation.
Variance and Standard Deviation Examples
Examples for finding variance and standard deviation are given below:
1)The height of several objects is given below:
300 mm, 340 mm, 380 mm, 430 mm, and 480 mm.
Find : The Variance and The Standard deviation.

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