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Unformatted text preview: formulae. Standard deviation is also called Root-Mean 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 square-root 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 deviation-Individual 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 d-stands for the deviation from assumed mean = (X-A) 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., X-A 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.

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