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 15 of 24
141. 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 values142. 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: Mean143. 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: b144. 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: Mean145. 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: 90146. 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: 24147. 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 values148. If β2=m4m22<3, the distribution is called______________?
- A. Normal
- B. Mesokurtic
- C. Leptokurtic
- D. Platykurtic
Explanation: β₂ = μ₄/μ₂² measures kurtosis, and β₂ < 3 indicates a flatter-than-normal distribution. Such a distribution is called platykurtic, whereas β₂ > 3 indicates leptokurtosis.
Correct answer: Platykurtic149. The degree of peakedness is called__________________?
- A. Dispersion
- B. Skewness
- C. Symmetry
- D. Kurtosis
Explanation: Kurtosis measures the degree of peakedness or flatness of a distribution. Skewness instead measures asymmetry around the centre.
Correct answer: Kurtosis150. Quartile Coefficient of skewness lies between______________?
- A. 0 and 1
- B. -1 and +1
- C. -1 and 0
- D. None of these
Explanation: Bowley’s quartile coefficient of skewness is bounded between −1 and +1 because it is based on quartile distances. Its sign indicates the direction of skewness.
Correct answer: -1 and +1