bus-stat-book1

Find out the deviations from the assumed mean ie x a

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Unformatted text preview: fd ) = N Example 9: Calculate the standard deviation from the following data. 14, 22, 9, 15, 20, 17, 12, 11 Solution: Deviations from actual mean. 2 Values (X) 14 22 9 15 20 17 12 11 120 120 X= =15 8 σ= -1 7 -6 0 5 2 -3 -4 Σ(x − x)2 n 140 8 = 17.5 = 4.18 = 158 1 49 36 0 25 4 9 16 140 Example 10: The table below gives the marks obtained by 10 students in statistics. Calculate standard deviation. Student Nos : 1 2 3 4 567 8 9 10 Marks : 43 48 65 57 31 60 37 48 78 59 Solution: (Deviations from assumed mean) Nos. Marks (x) d=X-A (A=57) 1 2 3 4 5 6 7 8 9 10 = ∑d − n -14 -9 8 0 -26 3 -20 -9 21 2 196 81 64 0 676 9 400 81 441 4 ∑d=-44 43 48 65 57 31 60 37 48 78 59 n = 10 ∑d2 σ= n d2 ∑d2 =1952 2 1952 −44 − 10 10 2 = 195.2 − 19.36 = 175.84 = 13.26 7.6.3 Calculation of standard deviation: Discrete Series: There are three methods for calculating standard deviation in discrete series: (a) Actual mean methods (b) Assumed mean method (c) Step-deviation method. 159 (a) Actual mean method: Steps: 1. Calculate the mean of the series. 2. Find deviations for various items from the means i.e., x- x = d. 3. Square the deviations (= d2 ) and multiply by the respective frequencies(f) we get fd2 4. Total to product (∑fd2 ) Then apply the formula: ∑ fd 2 ∑f If the actual mean in fractions, the calculation takes lot of time and labour; and as such this method is rarely used in practice. (b) Assumed mean method: Here deviation are taken not from an actual mean but from an assumed mean. Also this method is used, if the given variable values are not in equal intervals. Steps: 1. Assume any one of the items in the series as an assumed mean and denoted by A. 2. Find out the deviations from assumed mean, i.e, X-A and denote it by d. 3. Multiply these deviations by the respective frequencies and get the ∑fd 4. Square the deviations (d2 ). 5. Multiply the squared deviations (d2) by the respective frequencies (f) and get ∑fd2. 6. Substitute the values in the following formula: σ= ∑ fd 2 ∑ fd σ= − ∑f ∑f Where d = X −A , N = ∑f. 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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