bus-stat-book1

71 md 195 n 171 md 0106 161 median 755 mean deviation

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Unformatted text preview: mean and median from the following series. Age in years No.of persons 0-10 20 10-20 25 20-30 32 30-40 40 40-50 42 50-60 35 60-70 10 70-80 8 Also compute co-efficient of mean deviation. Solution: X m f 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 5 15 25 35 45 55 65 75 m−A c (A=35,C=10) 20 25 32 40 42 35 10 8 212 x = A+ ∑ fd × c N 32 = 35 + × 10 212 = 35 + d= -3 -2 -1 0 1 2 3 4 D= fd -60 -50 -32 0 42 70 30 32 32 m−x fD 31.5 21.5 11.5 1.5 8.5 18.5 28.5 38.5 630.0 537.5 368.0 60.0 357.0 647.5 285.0 308.0 3193.0 320 = 35 + 1.5 = 36.5 212 154 ∑f D 3193 = 15.06 N 212 Calculation of median and M.D. from median M.D. = = X m f c.f |D| = |m-Md| f |D| 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 5 15 25 35 45 55 65 75 20 25 32 40 42 35 10 8 20 45 77 117 159 194 204 212 32.25 22.25 12.25 2.25 7.75 17.75 27.75 37.75 Total 645.00 556.25 392.00 90.00 325.50 621.25 277.50 302.00 3209.50 N 212 = = 106 2 2 l = 30, m = 77, f = 40, c = 10 N −m 2 Median = l + ×c f 106 - 77 = 30 + × 10 40 29 = 30 + 4 = 30 + 7.25 = 37.25 ∑f | D | M. D. = N 3209.5 = = 15.14 212 M.D Coefficient of M.D = Median 15.14 = 0.41 = 37.25 155 7.5.6 Merits and Demerits of M.D : Merits: 1. It is simple to understand and easy to compute. 2. It is rigidly defined. 3. It is based on all items of the series. 4. It is not much affected by the fluctuations of sampling. 5. It is less affected by the extreme items. 6. It is flexible, because it can be calculated from any average. 7. It is better measure of comparison. Demerits: 1. It is not a very accurate measure of dispersion. 2. It is not suitable for further mathematical calculation. 3. It is rarely used. It is not as popular as standard deviation. 4. Algebraic positive and negative signs are ignored. It is mathematically unsound and illogical. 7.6 Standard Deviation and Coefficient of variation: 7.6.1 Standard Deviation : Karl Pearson introduced the concept of standard deviation in 1893. It is the most important measure of dispersion and is widely used in many statistical...
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