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 9 of 55
81. If any value in the data is zero, then which of the following average vanishes ______________?
- A. A.M.
- B. G.M.
- C. Mode
- D. None of these
Explanation: The geometric mean is the nth root of the product of all observations, so any zero makes that product zero and the geometric mean zero. The arithmetic mean and mode do not necessarily vanish when one observation is zero.
Correct answer: G.M.82. The sum of deviations of observations is zero, when deviations are taken from __________?
- A. Mean
- B. Median
- C. Mode
- D. None of these
Explanation: Deviations from the arithmetic mean balance exactly: positive and negative deviations sum to zero. Deviations from the median or mode do not generally have this property.
Correct answer: Mean83. If any value in the data is negative, then it is impossible to calculate _______?
- A. A.M.
- B. Mode
- C. H.M.
- D. G.M.
Explanation: The usual real-valued geometric mean is defined for non-negative observations, so a negative value makes it unavailable under the standard definition. Arithmetic mean and mode can still be calculated, while the harmonic mean mainly fails when a value is zero.
Correct answer: G.M.84. G.M. are set of 'n' values product of the nth roots of the ______________?
- A. Given value
- B. All +ve, -Ve value
- C. Zero reject
- D. None of these
Explanation: For n observations, the geometric mean is the nth root of their product, written as (x₁x₂⋯xₙ)^(1/n). Thus the intended completion is “given values,” although the option should use the plural form.
Correct answer: Given value85. Average is good if it is easy to ____________?
- A. Change
- B. Capable
- C. Understand
- D. Clear
Explanation: An average is useful only when its value and meaning can be understood readily by the people using it. Ease of change is undesirable because a good average should be stable.
Correct answer: Understand86. G.M. of 2,4,8 is ______?
- A. 6
- B. 4
- C. 14/3
- D. 8
Explanation: The geometric mean is the cube root of the product: (2 × 4 × 8)^(1/3) = 64^(1/3) = 4. Therefore, option b is correct.
Correct answer: 487. Median is always central value even if the data is _______?
- A. Unassigned
- B. Arranged
- C. Continuous
- D. Discrete
Explanation: The median is the middle position only after the observations have been arranged in ascending or descending order. Without ordering, the central observation cannot be identified reliably.
Correct answer: Arranged88. Harmonic mean cannot be calculated if any one of the values in the data is _____________?
- A. Zero
- B. Negative
- C. Positive
- D. All sign
Explanation: The harmonic mean uses reciprocals, as in n divided by the sum of 1/x values. A zero observation would require division by zero, so the harmonic mean cannot then be calculated.
Correct answer: Zero89. Median is _______ than mean is a positive skewed distribution?
- A. Great
- B. lesser
- C. Equal
- D. None of these
Explanation: In a positively skewed distribution, the long right tail pulls the mean above the median. Hence the median is lesser than the mean.
Correct answer: lesser90. The Harmonic Mean of two number is 'a' and 'b' is given by ____________?
- A. a+b/2
- B. 2ab/a+b
- C. √ab
- D. None of these
Explanation: For two values, the harmonic mean is obtained by dividing twice their product by their sum: 2ab/(a+b). This differs from the geometric mean, which is √ab.
Correct answer: 2ab/a+b