All Free Statistics MCQs with Answers

• A. Arbitrary value
• B. Mean
• C. Mode
• D. G.M.

Explanation: The sum of squared deviations is minimized when deviations are measured from the arithmetic mean, a fundamental property of the mean.

• A. Mean
• B. Mode
• C. Median
• D. H.M.

Explanation: The mode is the value or category occurring with the highest frequency in a data set.

• A. Decease
• B. Smaller
• C. Largest
• D. Increase

Explanation: Adding a constant to every observation adds the same constant to the arithmetic mean: mean(new data) = mean(old data) + 10.

• A. Vary
• B. Negative
• C. Affected
• D. Not affected

Explanation: A change of origin adds or subtracts a constant, while a change of scale multiplies the mean, so the arithmetic mean is affected by both.

• A. 4
• B. 8
• C. 2
• D. 0

Explanation: All six observations equal 4, so every deviation from the mean is zero.

• A. 20
• B. 5
• C. 2.5
• D. 0

Explanation: Dividing every observation by 2 divides the standard deviation by 2 and the variance by its square, 2². Thus the new variance is 10/4 = 2.5.

• A. 6
• B. Zero
• C. 3
• D. 2

Explanation: The mean of 18, 12, and 15 is 15; their absolute deviations are 3, 3, and 0. Their average is (3 + 3 + 0)/3 = 2.

• A. 1
• B. -1
• C. 3
• D. 0

Explanation: Variance is an average of squared deviations from the mean, so it cannot be negative.

• A. 8
• B. 3
• C. 24
• D. None of these

Explanation: For a linear transformation Y = aX + b, the standard deviation is |a| times the standard deviation of X; the constant b has no effect.

• A. Origin
• B. Scale
• C. Both
• D. None of these

Explanation: Adding or subtracting a constant changes the origin but leaves every deviation from the mean unchanged, so variance remains unchanged.

• A. 1
• B. 0
• C. Mean
• D. Mode
• E. Median

Explanation: When all observations are equal, each observation has zero deviation from the mean.

• A. Zero
• B. Positive
• C. Least
• D. None of these

Explanation: The median minimizes the sum of absolute deviations because at least half the observations lie on each side of it.

• A. Standard deviation
• B. Variation
• C. C.V.
• D. Range

Explanation: Range is the simplest measure of dispersion because it uses only the largest and smallest observations: range equals maximum minus…

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

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

• A. Relative Dispersion
• B. Observation
• C. Absolute
• D. Items

Explanation: Standard deviation is calculated from the deviations of all observations from their mean, so changing any observation can affect it.

• A. Coefficient of dispersion
• B. Mean coefficient
• C. Coefficient of variance
• D. Q.D.

Explanation: Consistency is commonly compared using the coefficient of variation, calculated as standard deviation divided by the mean, usually…

• A. Skewed
• B. Flatness
• C. Normal
• D. Moment

Explanation: Flatness refers to kurtosis, which describes the shape of a distribution relative to the normal distribution.

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

Explanation: A symmetrical distribution has balanced tails, so its skewness is zero.

• A. Easy
• B. mathematically
• C. Abjectly
• D. Algebraic

Explanation: Quartile deviation depends on the first and third quartiles and is not readily suitable for algebraic manipulation.

• A. Quartile deviation
• B. Mean dervation
• C. Mean coefficient
• D. Coefficient of quartile Deviation

Explanation: Relative dispersion is expressed as a coefficient, such as the coefficient of quartile deviation, rather than the quartile deviation…