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.
Last updated
238 questions · page 17 of 24
161. In uni-model distribution, if mode is less than mean_______________?
- A. Symmetrical
- B. Normal
- C. Positively Skewed
- D. Negatively Skewed
Explanation: In a positively skewed unimodal distribution, the long right tail pulls the mean to the right of the mode. Thus mean greater than mode indicates positive skewness.
Correct answer: Positively Skewed162. The Coefficient of Skewness is always zero for ____________ distribution?
- A. Symmetrical
- B. Skewed
- C. All of above
- D. None of these
Explanation: A symmetrical distribution has equal balancing tails, giving a skewness coefficient of zero. A skewed distribution generally has a positive or negative coefficient.
Correct answer: Symmetrical163. Second moment about mean is_______________?
- A. Standard Deviation
- B. Variance
- C. Coefficient of Variation
- D. None of these
Explanation: The second central moment is the average squared deviation from the mean, which is the variance. Standard deviation is its square root.
Correct answer: Variance164. _____________is used to compare the variation or dispersion in two or more sets of data even though they are measured in different units?
- A. Range
- B. Standard Deviation
- C. Coefficient of Variation
- D. Mean Deviation
Explanation: The coefficient of variation compares standard deviation with the mean, usually as a percentage, so it is suitable for data measured in different units or with different scales. Range and standard deviation retain the original measurement units.
Correct answer: Coefficient of Variation165. If the standard deviation of the values 2, 4, 6, 8 is 2.58, then the standard deviation of the values 4, 6, 8, 10 is_______________?
- A. 0
- B. 2.58
- C. 5
- D. 4.66
- E. 2.33
Explanation: Adding 2 to every observation changes the mean but not the deviations from the mean, so the standard deviation remains 2.58. This invariance holds for either population or sample standard deviation.
Correct answer: 2.58166. Standard deviation is calculated from the Harmonic Mean (HM) ________________?
- A. Always
- B. Sometimes
- C. Never
- D. None of these
Explanation: Standard deviation is based on deviations from the arithmetic mean, not the harmonic mean. Therefore, it is never calculated from the harmonic mean in the usual definition.
Correct answer: Never167. If a and b are two constants, then Var(a+bX) is_______________?
- A. a±bVar(X)
- B. Var(a)±Var(X)
- C. ±bVar(X)
- D. b2Var(X)
- E. (a±b)Var(X)
Explanation: Adding the constant a shifts every value but does not change spread, while multiplying by b multiplies variance by b². Hence Var(a+bX) = b²Var(X).
Correct answer: b2Var(X)168. The sum of squared deviations of a set of n values from their mean is__________________?
- A. Zero
- B. Maximum
- C. Least
- D. None
Explanation: The arithmetic mean is the value that minimizes the sum of squared deviations. Thus, deviations squared from the mean have the least possible sum, not necessarily a zero sum.
Correct answer: Least169. The measure of dispersion is changed by a change of_____________?
- A. Origin
- B. Scale
- C. Algebraic Signs
- D. None
Explanation: Changing the origin adds or subtracts a constant and leaves spread unchanged, but changing the scale multiplies dispersion measures. Therefore, dispersion is affected by a change of scale.
Correct answer: Scale170. The algebraic sum of deviations from mean is_____________?
- A. Maximum
- B. Zero
- C. Minimum
- D. Undefined
Explanation: Positive and negative deviations from the arithmetic mean balance each other exactly. Therefore, their algebraic sum is zero.
Correct answer: Zero