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 19 of 55
181. Lack of symmetry is called_______________?
- A. Absolute Dispersion
- B. Relative Dispersion
- C. Skewness
- D. Non of these
Explanation: Skewness measures the lack of symmetry in a distribution. Absolute and relative dispersion measure spread, not asymmetry.
Correct answer: Skewness182. If right tail is longer than left tail then distribution is called _________________?
- A. Negatively Skewed
- B. Positively Skewed
- C. All of above
- D. None of these
Explanation: A longer right tail indicates positive, or right, skewness, so the mean is typically pulled above the median. Negative skewness has the longer tail on the left.
Correct answer: Positively Skewed183. ______________is based on all observations of data?
- A. Median
- B. Mode
- C. Mean
- D. None of these
Explanation: The arithmetic mean is calculated by adding all observations and dividing by their number, so every value contributes. The median and mode depend on position or frequency rather than all observations.
Correct answer: Mean184. 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 Skewed185. 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: Symmetrical186. 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: Variance187. _____________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 Variation188. 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: 2.58189. 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: Never190. 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)