Free Measures of Central Tendency and Dispersion MCQs with Answers
30 Measures of Central Tendency and Dispersion MCQs from Quantitative Methods, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Central tendency includes mean, weighted mean, median and mode for raw and grouped data. Dispersion covers range, quartiles, interquartile range, variance, standard deviation and coefficient of variation, including the effect of changes in scale and the distinction between a representative centre and the spread around it.
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30 questions · page 2 of 2
- A. 9.5
- B. 10.5
- C. 11.5
- D. 12.5
Explanation: After arranging the values, the middle two observations are 9 and 12. Since there are six observations, the median is their average, which…
Correct answer: 10.5- A. When all observations are distinct
- B. When all observations are equal
- C. When the median is zero
- D. When the range is maximum
Explanation: The arithmetic mean equals the geometric mean when every positive observation has the same value.
Correct answer: When all observations are equal- A. 2
- B. Square root of 10
- C. 3
- D. Square root of 5
Explanation: The mean is 7, and the squared deviations are 9, 1, 1 and 9. Their population average is 5, so the population standard deviation is the…
Correct answer: Square root of 5- A. 2.0
- B. 2.4
- C. 3.0
- D. 3.2
Explanation: The median is 6. The absolute deviations from 6 total 12, and dividing by the five observations gives a mean deviation of 2.4.
Correct answer: 2.4- A. 5
- B. 6
- C. 12
- D. 24
Explanation: The semi-interquartile range is half the difference between the third and first quartiles. Thus, it is (18 minus 6) divided by 2, or 6.
Correct answer: 6- A. Variance
- B. Coefficient of variation
- C. Standard deviation
- D. Squared range
Explanation: Standard deviation is the square root of variance, so it retains the original measurement units.
Correct answer: Standard deviation- A. 50 percent
- B. 60 percent
- C. 75 percent
- D. 95 percent
Explanation: Chebyshev's theorem gives the minimum proportion as 1 minus 1 divided by k squared. For k equal to 2, this is 1 minus 1/4, or 75 percent.
Correct answer: 75 percent- A. n
- B. n minus 1
- C. n plus 1
- D. 2n
Explanation: The sample variance uses n minus 1 in the denominator to correct for the loss of one degree of freedom when the sample mean is estimated.
Correct answer: n minus 1- A. Mean is below median and mode
- B. Mean is above median and mode
- C. Mean, median and mode are equal
- D. Mean equals mode but not median
Explanation: A perfectly symmetrical unimodal distribution has its centre at the same point for all three measures.
Correct answer: Mean, median and mode are equal30. Which measure of central tendency is most appropriate for a nominal variable such as blood group?
- A. Arithmetic mean
- B. Median
- C. Geometric mean
- D. Mode
Explanation: Nominal categories have no meaningful numerical order or distance, so their most frequent category is summarized by the mode.
Correct answer: Mode