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 13 of 55
121. Second moment about mean is always equal to _____________?
- A. S.D.
- B. C.V.
- C. Variance
- D. Square
Explanation: The second moment about the mean is the average of squared deviations from the mean, which is the variance. Standard deviation is obtained by taking the square root of variance.
Correct answer: Variance122. which is poor measure of dispersion in open-end distribution ________________?
- A. Quartile- deviation
- B. Semi-inter quartile range
- C. Range
- D. None of these
Explanation: Range depends only on the smallest and largest values, which are unavailable or open-ended in such distributions. Quartile deviation can still be calculated from the central quartiles, making range the poor measure.
Correct answer: Range123. The frequency distribution mean > Median > Mode is called __________?
- A. Negatively
- B. Symmetrical
- C. +vely
- D. One
Explanation: In a positively skewed distribution, the long right tail pulls the mean furthest right, giving mean > median > mode. Negative skewness reverses this order.
Correct answer: +vely124. suppose for 40 observation, the variance is 50. If all the observation are increased by 20, the variance of these increased observation will be_________?
- A. 50
- B. 70
- C. 50/20
- D. 50-20=30
Explanation: Adding the same constant to every observation shifts the distribution without changing its spread. Hence the variance remains 50, even though the mean increases by 20.
Correct answer: 50125. Standard deviation is always calculated from _____________?
- A. Mean
- B. Median
- C. Mode
- D. G.M.
Explanation: Standard deviation is conventionally calculated as the square root of the mean squared deviations from the arithmetic mean. Median-based measures such as mean deviation about the median are different statistics.
Correct answer: Mean126. The sum of the squares of deviations is the least when measured from____________?
- A. A.M.
- B. Median
- C. Mode
- D. G.M.
Explanation: The arithmetic mean minimizes the sum of squared deviations because the cross-product term vanishes when deviations are taken from the mean. This is the least-squares property of the mean.
Correct answer: A.M.127. If Skewed distribution the three averages mean, median and mode are ________?
- A. Identical
- B. Different
- C. Zero
- D. None of theseDownload Reference Apps
Explanation: In a skewed distribution, the mean, median, and mode generally do not coincide, although their relative positions indicate the direction of skewness. They are identical in a perfectly symmetric unimodal distribution.
Correct answer: Different128. The value of interval x ± S include _______________?
- A. 49.45%
- B. 95.45%
- C. 68.27%
- D. 99.73%
Explanation: For a normal distribution, the interval from the mean minus one standard deviation to the mean plus one standard deviation contains about 68.27% of observations. The 95.45% and 99.73% figures correspond to two and three standard deviations.
Correct answer: 68.27%129. The S.D. and variance are ____ of origine?
- A. Multiplied
- B. Variance
- C. Change
- D. Independent
Explanation: Changing the origin by adding or subtracting a constant does not change deviations from the centre, so neither variance nor standard deviation changes. Changing the measurement scale does affect them.
Correct answer: Independent130. In grouped data, the range is the difference between ________________?
- A. Two extreme class boundaries
- B. Two extreme class frequency
- C. Two extreme class limits
- D. None of these
Explanation: For grouped data, the range is estimated as the upper boundary of the highest class minus the lower boundary of the lowest class. Class frequencies do not determine the range.
Correct answer: Two extreme class boundaries