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 8 of 24
71. Coded method of calculation is only used in ___________?
- A. Median
- B. Combined mean
- C. A.M.
- D. None of these
Explanation: The coded or assumed-mean method simplifies calculation of the arithmetic mean by replacing observations with deviations from a chosen origin. It is not the standard method for finding a median or mode.
Correct answer: A.M.72. If any value in the data is zero, then it is not possible to have _______?
- A. A.M.
- B. Medain
- C. Mode
- D. H.M.
Explanation: The harmonic mean uses reciprocals, and a zero observation has a reciprocal that is undefined. Therefore, a dataset containing zero cannot have a valid harmonic mean.
Correct answer: H.M.73. In moderately skewed distribution if _________________?
- A. Mode = 3 median - 2 mean
- B. Mode = 2 median -3 mean
- C. Median = 2 median-3 mean
- D. Mean- mode
Explanation: For a moderately skewed distribution, Pearson’s empirical relation is Mean − Mode ≈ 3(Mean − Median), which rearranges to Mode ≈ 3 Median − 2 Mean. Thus option a gives the standard formula.
Correct answer: Mode = 3 median - 2 mean74. Third quartile = Q3 = ____________?
- A. P33
- B. D3
- C. Median
- D. None of these
Explanation: The third quartile is the 75th percentile, written as Q3 = P75. Since P75 is not listed, none of these is correct.
Correct answer: None of these75. Mean is relatively ____ measure?
- A. Stable
- B. manipulation
- C. Change
- D. Group
Explanation: The arithmetic mean is relatively stable because it uses every observation and generally varies less from sample to sample than the mode. However, it can still be influenced by extreme values.
Correct answer: Stable76. __________ deviation taken from A.M. is always equal to zero?
- A. Mean
- B. Sum
- C. Average
- D. 2.D.
Explanation: The algebraic sum of deviations from the arithmetic mean is always zero: Σ(x − x̄) = 0. Individual deviations need not be zero, but their positive and negative values cancel.
Correct answer: Sum77. If the smallest observation in a data is decreased, the average which is not affected is______________?
- A. G.M.
- B. Median
- C. Mean
- D. Harmonic mean
Explanation: Reducing the smallest observation keeps it at the lower end of the ordered data, so the middle position and hence the median remain unchanged. Means, including the arithmetic, geometric, and harmonic means, are affected by changing an observation.
Correct answer: Median78. The sum of square of deviation is least when measured from ____________?
- A. Arbitrary value
- B. Mean
- C. Mode
- D. G.M.
Explanation: The sum of squared deviations is minimized when deviations are measured from the arithmetic mean, a fundamental property of the mean. Measuring from any other value produces a larger sum.
Correct answer: Mean79. The most frequent value in data is called ________________?
- A. Mean
- B. Mode
- C. Median
- D. H.M.
Explanation: The mode is the value or category occurring with the highest frequency in a data set. The mean and median are based on numerical position or magnitude rather than frequency alone.
Correct answer: Mode80. The arithmetic mean _________ by 10 if 10 is added to all values?
- A. Decease
- B. Smaller
- C. Largest
- D. Increase
Explanation: Adding a constant to every observation adds the same constant to the arithmetic mean: mean(new data) = mean(old data) + 10. Hence the mean increases by 10.
Correct answer: Increase