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 10 of 55
91. Sum of obsolete deviations from _____ is least?
- A. Mean
- B. Median
- C. Harmonic
- D. Mode
Explanation: The sum of absolute deviations is least when deviations are measured from the median. The mean instead minimizes the sum of squared deviations, so it is the tempting alternative.
Correct answer: Median92. We must arrange the data before calculating _________?
- A. Mean
- B. Median
- C. Mode
- D. G.M.
Explanation: The median depends on the middle position, so the observations must first be arranged in ascending or descending order. Mean and geometric mean do not require arranging the data.
Correct answer: Median93. The mode of the data 2,4,6,6,6,8 is _______________?
- A. 4
- B. 6
- C. 8
- D. 30
Explanation: The mode is the value occurring most frequently. Here, 6 appears three times, more often than any other value.
Correct answer: 694. 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.95. 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.96. 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 mean97. 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 these98. 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: Stable99. __________ 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: Sum100. 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: Median