Skewness of Frequency Distribution

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Skewness is the lack of symmetry in a frequency distribution. It measures the tendency of a distribution to depart from symmetry. When a distribution is not symmetric (bell-shaped), it is said to be s…

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1. Mean = Median = Mode (x̄ = M = M₀) 2. Quartiles are equidistant from median: (Q₃ - M) = (M - Q₁) 3. Bell-shaped frequency curve 4. Equal frequencies at equal distances from mode on both sides…

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Positive skewness occurs when the right tail of the frequency curve is more elongated. Characteristics: 1. Mean > Median > Mode (x̄ > M > M₀) 2. (Q₃ - M) > (M - Q₁) 3. Right tail is longer 4. Skewness…

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Negative skewness occurs when the left tail of the frequency curve is more elongated. Characteristics: 1. Mean < Median < Mode (x̄ < M < M₀) 2. (Q₃ - M) < (M - Q₁) 3. Left tail is longer 4. Skewness c…

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Absolute measure: Expressed in same units as the data, denoted by Sk. Cannot be used to compare different populations. Relative measure: Unit-free measure obtained by dividing absolute measure by appr…

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j = (x̄ - M₀)/s Where: j = coefficient of skewness x̄ = mean M₀ = mode s = standard deviation Used when distribution has a clear, single mode.

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j = 3(x̄ - M)/s Where: j = coefficient of skewness x̄ = mean M = median s = standard deviation Based on empirical relation: M₀ = 3M - 2x̄…

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j = (Q₃ + Q₁ - 2M)/(Q₃ - Q₁) Where: j = coefficient of skewness Q₁ = first quartile Q₃ = third quartile M = median Based on quartile positions and ranges from -1 to +1.