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D symbolically md n example 6 calculate mean deviation

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Unformatted text preview: x D = x − Md 100 150 200 250 360 490 500 600 671 3321 269 219 169 119 9 121 131 231 302 1570 260 210 160 110 0 130 140 240 311 1561 M.D from mean = ∑D n 1570 = = 174.44 9 M.D Co-efficient of M.D = x 174.44 = = 0.47 369 ∑D M.D from median = n 1561 = = 173.44 9 M.D 173.44 Co-efficient of M.D.= = = 0.48 Median 360 7.5.4 Mean Deviation – Discrete series: Steps: 1. Find out an average (mean, median or mode) 2. Find out the deviation of the variable values from the average, ignoring signs and denote them by D 3. Multiply the deviation of each value by its respective frequency and find out the total ∑ f D 151 ∑ f D by the total frequencies ∑f D M.D. = 4. Divide Symbolically, N N Example 7: Compute Mean deviation from mean and median from the following data: Height 158 159 160 161 162 163 164 165 166 in cms No. of 15 20 32 35 33 22 20 10 8 persons Also compute coefficient of mean deviation. Solution: Height No. of X persons f 158 15 159 20 160 32 161 35 162 33 163 22 164 20 165 10 166 8 195 x = A+ d= x- A A =162 fd -4 -3 -2 -1 0 1 2 3 4 |D| = |X- mean| - 60 - 60 - 64 - 35 0 22 40 30 32 - 95 ∑ fd N − 95 = 162 + = 162 – 0.49 = 161.51 195 ∑ f D = 338.59 = 1.74 M.D. = N 195 152 3.51 2.51 1.51 0.51 0.49 1.49 2.49 3.49 4.49 f|D| 52.65 50.20 48.32 17.85 16.17 32.78 49.80 34.90 35.92 338.59 M.D 1.74 = = 0.0108 161.51 X No. of D= persons c.f. X − Median f 15 15 3 20 35 2 32 67 1 35 102 0 33 135 1 22 157 2 20 177 3 10 187 4 8 195 5 195 Coefficient of M.D.= Height x 158 159 160 161 162 163 164 165 166 fD 45 40 32 0 33 44 60 40 40 334 th N +1 Median = Size of item 2 th 195 +1 = Size of item 2 = Size of 98 th item = 161 ∑ f D = 334 = 1.71 M.D = 195 N 1.71 M.D =.0106 = 161 Median 7.5.5 Mean deviation-Continuous series: The method of calculating mean deviation in a continuous series same as the discrete series.In continuous series we have to find out the mid points of the various classes and take deviation of these points from the average selected. Thus ∑f | D | M.D = N Coefficient of M.D. = 153 Where D = m - average M = Mid point Example 8: Find out the mean deviation from...
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