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 17 of 55
161. In a frequency distribution the last cumulative frequency is 500. Q3 must lie in_____________?
- A. 275th item
- B. 375th item
- C. 150th item
- D. 175th item
Explanation: The position of Q3 is 3(N+1)/4, or conventionally 3N/4 for grouped distributions. With N = 500, this gives the 375th item.
Correct answer: 375th item162. Find the median of the following datA. 160, 180, 200, 280, 300, 320, 400?
- A. 140
- B. 300
- C. 180
- D. 280
Explanation: The seven values are already ordered, so the median is the fourth value, 280. For an odd number of observations, the median occupies position (n+1)/2.
Correct answer: 280163. In a frequency distribution the last cumulative frequency is 300, Median shall lie in____________?
- A. 140th item
- B. 130th item
- C. 160th item
- D. 150th item
Explanation: For a distribution containing 300 observations, the median position is conventionally N/2 = 300/2 = 150, so it lies at the 150th item. More exact ungrouped-data conventions may average the 150th and 151st observations.
Correct answer: 150th item164. Given the N values in a series, the geometric mean is______________?
- A. The third root of the product of N values
- B. The square root of the product of N values
- C. The fourth root of the product of N values
- D. The Nth root of the product of N values
Explanation: For N values, the geometric mean is the Nth root of their product: GM = (x₁x₂...xₙ)^(1/N). The root must match the number of values, not always be a square, cube or fourth root.
Correct answer: The Nth root of the product of N values165. The sum of squared deviation is least from_________________?
- A. Median
- B. Mean
- C. Mode
- D. Standard Deviation
Explanation: The arithmetic mean minimizes the sum of squared deviations because deviations above and below it balance in the least-squares sense. The median instead minimizes the sum of absolute deviations.
Correct answer: Mean166. The mean of a constant "b" is_________________?
- A. Zero
- B. b
- C. None
Explanation: Every observation in a constant series equals b, so their total is nb and dividing by n gives a mean of b.
Correct answer: b167. Sum of deviations will be zero if it is taken from_________________?
- A. Mean
- B. Mode
- C. Median
- D. Standard Deviation
Explanation: The algebraic sum of deviations from the arithmetic mean is always zero because positive and negative deviations balance each other. This property does not generally hold when deviations are taken from the mode or median.
Correct answer: Mean168. The mean of 10 numbers is 9, then sum of these numbers will be__________________?
- A. 9
- B. 0.9
- C. 70
- D. 90
Explanation: Since mean = sum/n, the sum equals mean × number of observations = 9 × 10 = 90. The value 9 is the mean itself, not the total.
Correct answer: 90169. For a certain distribution if ∑(x−2)=18,∑(x−24)=0,∑(x−28)=−24) then arithmetic mean is_______________?
- A. 21
- B. 24
- C. 28
- D. 0
Explanation: Because ∑(x − 24) = 0, 24 is the arithmetic mean, using the property that deviations from the mean sum to zero. The other supplied sums are consistent with the same mean when the number of observations is positive.
Correct answer: 24170. The calculation of mean and variance is based on______________?
- A. Small values only
- B. Large values only
- C. Extreme values only
- D. All values
Explanation: Both the mean and variance use every observation in the dataset: the mean sums all values, while variance uses every squared deviation from the mean. Ignoring values would change these measures.
Correct answer: All values