bus-stat-book1

2 find out the deviations from assumed mean ie x a

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Unformatted text preview: Example 11: Calculate Standard deviation from the following data. X: 20 22 25 31 35 40 42 f: 5 12 15 20 25 14 10 160 45 6 Solution: Deviations from assumed mean x f d = x –A (A = 31) -11 5 20 -9 12 22 -6 15 25 0 20 31 4 25 35 9 14 40 11 10 42 14 6 45 N=107 σ= ∑ fd 2 ∑ fd − ∑f ∑f d2 fd fd2 121 81 36 0 16 81 121 196 -55 -108 -90 0 100 126 110 84 ∑fd=167 605 972 540 0 400 1134 1210 1176 ∑fd2 =6037 2 2 = = = 6037 167 − 107 107 56.42 − 2.44 53.98 = 7.35 (c) Step-deviation method: If the variable values are in equal intervals, then we adopt this method. Steps: 1. Assume the center value of the series as assumed mean A x−A 2. Find out d = , where C is the interval between each C value 3. Multiply these deviations d’ by the respective frequencies and get ∑fd 4. Square the deviations and get d 2 5. Multiply the squared deviation (d 2 ) by the respective frequencies (f) and obtain the total ∑fd 2 161 6. Substitute the values in the following formula to get the standard deviation. Example 12: Compute Standard deviation from the following data Marks : 10 20 30 40 50 No.of students: 8 12 20 10 7 Solution: Marks x F fd x − 30 d= 10 -16 -2 8 10 -12 -1 12 20 0 0 20 30 10 1 10 40 14 2 7 50 9 3 3 60 N=60 Σ fd =5 60 3 fd 2 32 12 0 10 28 27 Σ fd 2 = 109 2 = 109 5 - × 10 60 60 = 1.817 - 0.0069 × 10 = 1.8101 × 10 = 1.345 × 10 = 13.45 7.6.4 Calculation of Standard Deviation –Continuous series: In the continuous series the method of calculating standard deviation is almost the same as in a discrete series. But in a continuous series, mid-values of the class intervals are to be found out. The step- deviation method is widely used. 162 The formula is, d= m−A , C- Class interval. C Steps: 1.Find out the mid-value of each class. 2.Assume the center value as an assumed mean and denote it by A m−A 3.Find out d = C 4.Multiply the deviations d by the respective frequencies and get Σfd 5.Square the deviations and get d 2 6.Multiply the squared deviations (d 2) by the respec...
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