Standard Deviation Calculator
Standard Deviation Calculator
For a given data set standard deviation is defined as the measurement of the
spread of data or sometimes it is describe as the distribution of the data of a data
set .
It is used for defining the diversity of data in probability and statistics. It is
calculated on the basis of average mean or mode that how much the value of a
given data set is dispersed.
If the calculated standard deviation is less that means the dispersion of the data is
low means it is very close to the mean or mode value and if the value of standard
deviation is more, that means the value of the data set is much more dispersed.
In the statistics calculation of standard deviation is very much important and also
very much in demand.
Standard Deviation is the part of statistics that is defined in the data set of value
that is the diversity of the value.
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It is widely used to find out the variability of the values. It is defined the variation
from the mean value or define the deviation from average value. Standard
deviation helps to find the tendency of the values.
Standard deviation calculator is an online tool that helps in finding out the analysis
of data in terms of measure of the deviation or measure of the spread of the data
set.
That is used as the statistics or probability tool also. standard deviation calculator
defines the dispersion of the data in form of Populated standard deviation or
variance etc.
For specifying the standard deviation there is a symbol that is a sigma symbol (s)
and known as the standard deviation and there is another way of defining the
standard deviation is square root of variance that is defined as (s2).
We take some examples of standard deviation for understanding it, but before this
we have to define the standard deviation for a given distribution as follows:
For random variable (a), mean value is defined as `m' that is denoted in form of E |
a | = m.
Where `E' denotes the average value of `a' and formula for standard deviation is
(s) = E (a - m )2.
Sometimes standard deviation is calculated by using the formula of variance as
square root of the variance is equals to the standard deviation.
Example: There is a given data set that defines the variable as:
Variable: d1 d2 d3 d4 d5 d6
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Value: 3 4 4 5 6 8
Then find out the standard deviation for the values of given data set?
Solution: First of all we find the average value for the data of data set as a 6i = 1
d i.
That is defined as d1 + d2 + d3 + d4 + d5 + d6 = 3 + 4 + 4 + 5 + 6 + 8 = 30,
Mean value is m = a 6i= 1( d i) / n = 30 / 6 = 5.
After finding the value of mean find the variance as s2 = a (a - m)2 / n.
The above equation can be simplified to find the standard deviation s2 = a a2 /
n - m2.
s2that is equals to 2.67 and standard deviation is equals to 1.63.


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