All Free Statistics MCQs with Answers
Every Statistics question in the bank, across all chapters, each with the correct answer and a written explanation. Free and unlimited, with no account needed.
545 questions · page 11 of 55
101. The sum of square of deviation is least when measured from ____________?
- 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. Measuring from any other value produces a larger sum.
Correct answer: Mean102. The most frequent value in data is called ________________?
- 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. The mean and median are based on numerical position or magnitude rather than frequency alone.
Correct answer: Mode103. The arithmetic mean _________ by 10 if 10 is added to all values?
- 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. Hence the mean increases by 10.
Correct answer: Increase104. Arithmetic mean is _________ by change of origin and scale of measurement?
- 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. This differs from variance, which is unaffected by origin but changes with scale.
Correct answer: Affected105. Mean deviation, Variance and Standard Deviation of the values 4,4,4,4,4,4 is_______________?
- A. 4
- B. 8
- C. 2
- D. 0
Explanation: All six observations equal 4, so every deviation from the mean is zero. Therefore, mean deviation, variance, and standard deviation are all 0.
Correct answer: 0106. The variance of 5 numbers is 10. If each number is divided by 2, then variance of new number is_____________?
- 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.
Correct answer: 2.5107. The mean deviation of the values, 18, 12, 15, is_______________?
- 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.
Correct answer: 2108. Lowest value of variance can be____________?
- A. 1
- B. -1
- C. 3
- D. 0
Explanation: Variance is an average of squared deviations from the mean, so it cannot be negative. Its minimum value is 0, reached when all observations are identical.
Correct answer: 0109. If Y=-8X - 5 and SD of X is 3, then SD of Y is______________?
- 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. Hence SD(Y) = |-8| × 3 = 24.
Correct answer: 24110. Variance remains unchanged by change of_____________?
- 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. Changing the scale by a factor k changes variance by k².
Correct answer: Origin