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 11 of 24
101. 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: 50102. 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: Mean103. 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.104. 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: Different105. 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%106. 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: Independent107. 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 boundaries108. Relative measure of skewness was introduced by _____________?
- A. Rowely
- B. Lack
- C. Karl Person
- D. Mode
Explanation: Karl Pearson introduced a widely used relative measure of skewness, calculated from the relationship among the mean, mode and standard deviation. The option spells Pearson incorrectly but clearly refers to Karl Pearson.
Correct answer: Karl Person109. The degree to which numerical data tend to spread about an average value is a________________?
- A. Range
- B. variance
- C. Minimum
- D. Dispersion
Explanation: Dispersion describes the extent to which observations spread around a central value. Range and variance are individual measures of dispersion, while dispersion is the general concept.
Correct answer: Dispersion110. Range of 5,5,5,5, is ________________?
- A. 0
- B. 5
- C. 25
- D. None of these
Explanation: Range equals the largest observation minus the smallest observation. Since both are 5, the range is 5 − 5 = 0.
Correct answer: 0