bus-stat-book1

# 2 find out the deviations from assumed mean ie x a

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online