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Unformatted text preview: formulae. Standard deviation is also
called RootMean Square Deviation. The reason is that it is the
square–root of the mean of the squared deviation from the
arithmetic mean. It provides accurate result. Square of standard
deviation is called Variance.
Definition:
It is defined as the positive squareroot of the arithmetic
mean of the Square of the deviations of the given observation from
their arithmetic mean.
The standard deviation is denoted by the Greek letter σ (sigma)
7.6.2 Calculation of Standard deviationIndividual Series :
There are two methods of calculating Standard deviation in
an individual series.
a) Deviations taken from Actual mean
b) Deviation taken from Assumed mean
156 a) Deviation taken from Actual mean:
This method is adopted when the mean is a whole number.
Steps:
1. Find out the actual mean of the series ( x )
2. Find out the deviation of each value from the mean
3.Square the deviations and take the total of squared
deviations ∑x2 ∑ x2 4. Divide the total ( ∑x2 ) by the number of observation n ∑ x2 The square root of is standard deviation.
n ∑ x2 Σ(x − x) 2
or n
n
b) Deviations taken from assumed mean:
This method is adopted when the arithmetic mean is
fractional value.
Taking deviations from fractional value would be a very
difficult and tedious task. To save time and labour, We apply short
–cut method; deviations are taken from an assumed mean. The
formula is: Thus σ = ∑d2 ∑d σ=
− N
N
Where dstands for the deviation from assumed mean = (XA)
Steps:
1. Assume any one of the item in the series as an average (A)
2. Find out the deviations from the assumed mean; i.e., XA
denoted by d and also the total of the deviations ∑d
3. Square the deviations; i.e., d2 and add up the squares of
deviations, i.e, ∑d2
4. Then substitute the values in the following formula:
2 157 ∑d2 ∑d −
σ= n
n
Note: We can also use the simplified formula for standard
deviation.
1
2
n ∑ d 2 − (∑ d )
=
n
For the frequency distribution
c
2
N ∑ fd 2 − (∑...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.
 Winter '08
 Moshiri
 Business

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