Free Descriptive Statistics MCQs with Answers
238 Descriptive Statistics MCQs from Statistics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
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238 questions · page 9 of 24
81. 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: Affected82. 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: 083. 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: 2.584. 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: 285. 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: 086. 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: 2487. 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: Origin88. If all values are same then the measure of dispersion will be?
- A. 1
- B. 0
- C. Mean
- D. Mode
- E. Median
Explanation: When all observations are equal, each observation has zero deviation from the mean. Consequently every usual measure of dispersion, including range, variance, and standard deviation, is 0.
Correct answer: 089. The sum of absolute deviations from median is _____?
- 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. Therefore, absolute deviations are least when measured from the median.
Correct answer: Least90. ________ is the simplest means of dispersion?
- 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 minimum. Standard deviation and the coefficient of variation require more calculation.
Correct answer: Range