All Free Statistics MCQs with Answers

• A. 275th item
• B. 375th item
• C. 150th item
• D. 175th item

Explanation: The position of Q3 is 3(N+1)/4, or conventionally 3N/4 for grouped distributions. With N = 500, this gives the 375th item.

• A. 140
• B. 300
• C. 180
• D. 280

Explanation: The seven values are already ordered, so the median is the fourth value, 280.

• A. 140th item
• B. 130th item
• C. 160th item
• D. 150th item

Explanation: For a distribution containing 300 observations, the median position is conventionally N/2 = 300/2 = 150, so it lies at the 150th item.

• A. The third root of the product of N values
• B. The square root of the product of N values
• C. The fourth root of the product of N values
• D. The Nth root of the product of N values

Explanation: For N values, the geometric mean is the Nth root of their product: GM = (x₁x₂...xₙ)^(1/N).

• A. Median
• B. Mean
• C. Mode
• D. Standard Deviation

Explanation: The arithmetic mean minimizes the sum of squared deviations because deviations above and below it balance in the least-squares sense.

• A. Zero
• B. b
• C. None

Explanation: Every observation in a constant series equals b, so their total is nb and dividing by n gives a mean of b.

• A. Mean
• B. Mode
• C. Median
• D. Standard Deviation

Explanation: The algebraic sum of deviations from the arithmetic mean is always zero because positive and negative deviations balance each other.

• A. 9
• B. 0.9
• C. 70
• D. 90

Explanation: Since mean = sum/n, the sum equals mean × number of observations = 9 × 10 = 90. The value 9 is the mean itself, not the total.

• A. 21
• B. 24
• C. 28
• D. 0

Explanation: Because ∑(x − 24) = 0, 24 is the arithmetic mean, using the property that deviations from the mean sum to zero.

• A. Small values only
• B. Large values only
• C. Extreme values only
• D. All values

Explanation: Both the mean and variance use every observation in the dataset: the mean sums all values, while variance uses every squared deviation…

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

Explanation: β₂ = μ₄/μ₂² measures kurtosis, and β₂ < 3 indicates a flatter-than-normal distribution.

• 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.

• 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…

• 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…

• 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…

• 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.