All Free Statistics MCQs with Answers

• A. Normal
• B. Mesokurtic
• C. Leptokurtic
• D. Platykurtic

Explanation: β₂ = μ₄/μ₂² measures kurtosis, and β₂ < 3 indicates a flatter-than-normal distribution. Such a distribution is called platykurtic, whereas β₂ > 3 indicates leptokurtosis.

• A. Dispersion
• B. Skewness
• C. Symmetry
• D. Kurtosis

Explanation: Kurtosis measures the degree of peakedness or flatness of a distribution. Skewness instead measures asymmetry around the centre.

• A. 0 and 1
• B. -1 and +1
• C. -1 and 0
• D. None of these

Explanation: Bowley’s quartile coefficient of skewness is bounded between −1 and +1 because it is based on quartile distances. Its sign indicates the direction of skewness.

• A. Range
• B. Standard Deviation
• C. Coefficient of Variation
• D. Mean Deviation

Explanation: The coefficient of variation, CV = standard deviation/mean × 100, compares relative variability and is therefore used to judge consistency. A smaller CV indicates more consistent performance, even when means differ.

• A. Zero
• B. Constant
• C. a
• D. None

Explanation: Every observation equal to the same constant has zero deviation from its mean, so the sum of squared deviations and hence the variance is zero.

• A. 5 Var(X)
• B. 4 Var(X)
• C. 4 Var(X)+3
• D. 5 Var(X)+3

Explanation: Variance is affected by the square of a multiplier but not by an added constant: Var(aX+b)=a²Var(X). Therefore Var(2X+3)=4Var(X).

• A. 20
• B. 5
• C. 2.5
• D. 5.5
• E. 0

Explanation: Dividing every observation by 2 divides the standard deviation by 2 and the variance by 2²=4. The new variance is therefore 10/4=2.5.

• A. Positive
• B. Negative
• C. 0
• D. 1

Explanation: Measures such as range, variance, standard deviation, and mean deviation are non-negative because they are based on distances or squared deviations. They may be zero when all observations are identical, but never negative.

• A. 100%
• B. 25%
• C. 20%
• D. None of these

Explanation: The coefficient of variation is (standard deviation ÷ mean)×100. Hence CV=(5/25)×100=20%.

• A. Zero
• B. 1
• C. Negative
• D. None of these

Explanation: The first central moment is the mean of deviations from the mean, and positive and negative deviations cancel exactly. Therefore the first moment about the mean is zero.