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# 57 100 fd 3 309 8343 8343 c3 27 3 n 100 100 fd

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Unformatted text preview: 83.43 × c3 = × 27 = 3 N 100 100 ∑ fd ' 4 809 65529 = = 655.29 × 81 = × c4 = µ4 N 100 100 Moments about mean µ1 = 0 µ2 = µ 2 − µ 1 2 = 15.57 – (2.61)2 = 15.57 – 6.81 = 8.76 µ3 = µ 3 – 3µ 2 µ 1 + 2 µ 13 = 83.43 – 3(2.61) (15.57)+2 (2.61)3 = 83.43 – 121.9 + 35.56 = −2.91 µ4 = µ 4 – 4µ 3 µ 1 + 6µ 2 µ 12 – 3 µ 14 = 665.29 – 4 (83.43) (2.61) + 6 (15.57) (2.61)2 − 3(2.61)4 = 665.29 – 871.01 + 636.39 – 139.214 = 291.454 173 µ = fd 4 7.9 Skewness: 7.9.1 Meaning: Skewness means ‘ lack of symmetry’ . We study skewness to have an idea about the shape of the curve which we can draw with the help of the given data.If in a distribution mean = median = mode, then that distribution is known as symmetrical distribution. If in a distribution mean ≠ median ≠ mode , then it is not a symmetrical distribution and it is called a skewed distribution and such a distribution could either be positively skewed or negatively skewed. a) Symmetrical distribution: Mean = Median = Mode It is clear from the above diagram that in a symmetrical distribution the values of mean, median and mode coincide. The spread of the frequencies is the same on both sides of the center point of the curve. b)Positively skewed distribution: Mode Median Mean It is clear from the above diagram, in a positively skewed distribution, the value of the mean is maximum and that of the mode is least, the median lies in between the two. In the positively skewed distribution the frequencies are spread out over a greater range of values on the right hand side than they are on the left hand side. 174 c) Negatively skewed distribution: Mean Median Mode It is clear from the above diagram, in a negatively skewed distribution, the value of the mode is maximum and that of the mean is least. The median lies in between the two. In the negatively skewed distribution the frequencies are spread out over a greater range of values on the left hand side than they are on the right hand side. 7.10 Measures of skewness: The important measures of skewness are (i) Karl – Pearason’ s coefficient of skewness (ii) Bowle...
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