Skewness of Frequency Distribution — Flashcards
Gujarat Board · Class 11 · Statistics
22 flashcards for Skewness of Frequency Distribution (Gujarat Board Class 11 Statistics) to test yourself on key terms and facts.
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What is skewness in a frequency distribution?
Answer
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…
What are the characteristics of a symmetric frequency distribution?
Answer
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…
What is positive skewness and what are its characteristics?
Answer
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…
What is negative skewness and what are its characteristics?
Answer
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…
What is the difference between absolute measure and relative measure of skewness?
Answer
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…
State Karl Pearson's formula for coefficient of skewness when mode is well-defined.
Answer
j = (x̄ - M₀)/s Where: j = coefficient of skewness x̄ = mean M₀ = mode s = standard deviation Used when distribution has a clear, single mode.
State Karl Pearson's formula for coefficient of skewness when mode is ill-defined or multiple modes exist.
Answer
j = 3(x̄ - M)/s Where: j = coefficient of skewness x̄ = mean M = median s = standard deviation Based on empirical relation: M₀ = 3M - 2x̄…
State Bowley's formula for coefficient of skewness.
Answer
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.
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