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 16 of 24
151. ____________ is used to criterion of consistency i.e for consistence performance?
- A. Range
- B. Standard Deviation
- C. Coefficient of Variation
- D. Mean Deviation
Explanation: The coefficient of variation, CV = standard deviation/mean × 100, compares relative variability and is therefore used to judge consistency. A smaller CV indicates more consistent performance, even when means differ.
Correct answer: Coefficient of Variation152. The variance of a constant is_______________?
- A. Zero
- B. Constant
- C. a
- D. None
Explanation: Every observation equal to the same constant has zero deviation from its mean, so the sum of squared deviations and hence the variance is zero.
Correct answer: Zero153. Var(2X+3) is________________?
- A. 5 Var(X)
- B. 4 Var(X)
- C. 4 Var(X)+3
- D. 5 Var(X)+3
Explanation: Variance is affected by the square of a multiplier but not by an added constant: Var(aX+b)=a²Var(X). Therefore Var(2X+3)=4Var(X).
Correct answer: 4 Var(X)154. The variance of 5 numbers is 10. If each number is divided by 2, then the variance of new numbers is______________?
- A. 20
- B. 5
- C. 2.5
- D. 5.5
- E. 0
Explanation: Dividing every observation by 2 divides the standard deviation by 2 and the variance by 2²=4. The new variance is therefore 10/4=2.5.
Correct answer: 2.5155. The measure of Dispersion can never be________________?
- A. Positive
- B. Negative
- C. 0
- D. 1
Explanation: Measures such as range, variance, standard deviation, and mean deviation are non-negative because they are based on distances or squared deviations. They may be zero when all observations are identical, but never negative.
Correct answer: Negative156. If mean is 25 and standard deviation is 5 then C.V (Coefficient of variation) is_______________?
- A. 100%
- B. 25%
- C. 20%
- D. None of these
Explanation: The coefficient of variation is (standard deviation ÷ mean)×100. Hence CV=(5/25)×100=20%.
Correct answer: 20%157. The first moment about means is always_________________?
- A. Zero
- B. 1
- C. Negative
- D. None of these
Explanation: The first central moment is the mean of deviations from the mean, and positive and negative deviations cancel exactly. Therefore the first moment about the mean is zero.
Correct answer: Zero158. 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: Skewness159. 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 Skewed160. ______________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: Mean