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 16 of 55
151. The Harmonic Mean of any two numbers is________________?
- A. a+b2
- B. 2aba+b
- C. ab−−√
- D. a+b
Explanation: For two positive numbers, the harmonic mean is the reciprocal of the average of their reciprocals: 2ab divided by a+b. Thus option b gives the required formula.
Correct answer: 2aba+b152. Which of the following Measure of averages is affected by extreme (very small or very largE. values in data set?
- A. Geometric Mean
- B. Median
- C. Arithmetic Mean
- D. Harmonic Mean
- E. Mode
Explanation: The arithmetic mean uses every observation, so an extremely large or small value directly pulls it upward or downward. The median and mode are generally less affected by such extremes.
Correct answer: Arithmetic Mean153. Geometric means of X1 and X2 is________________?
- A. X1+X2
- B. X1+X2x
- C. X1+X2−−−−−−−√
- D. X1×X2−−−−−−−√
- E. X1−−−√+X2−−−√
Explanation: For two values, the geometric mean is the square root of their product, √(X₁X₂). Adding the values gives the arithmetic mean expression, not the geometric mean.
Correct answer: X1×X2−−−−−−−√154. Which of the following Measure of Averages is not based on all the values given in the data set?
- A. Arithmetic Mean
- B. Geometric Mean
- C. Median
- D. Mode
- E. Both C. and D.
Explanation: The median depends mainly on the middle position after ordering, and the mode depends on the most frequent value, so neither necessarily uses every observation. Therefore both C and D are correct.
Correct answer: Both C. and D.155. If 10% is added to each value of variable, the geometric mean of new variable is added by_______________?
- A. 5%
- B. 10%
- C. No Change
- D. 110%
- E. 90%
Explanation: Multiplying every observation by 1.10 multiplies the geometric mean by 1.10 as well. Hence the new geometric mean is 110% of the old one, an increase of 10%.
Correct answer: 10%156. The Geometric Mean of -2, 4, 03, 6, 0 will be______________?
- A. -3
- B. 0
- C. 3
- D. Cannot be Computed
- E. None of these
Explanation: A real geometric mean is ordinarily defined for positive observations; the listed data include both a negative value and zero. Consequently, its real geometric mean cannot be computed.
Correct answer: Cannot be Computed157. Which of the following cannot be less than zero (negative)?
- A. Median
- B. Geometric Mean
- C. Arithmetic Mean
- D. Harmonic Mean
- E. Mode
Explanation: Under the standard definition, the geometric mean is used for positive observations and therefore cannot be negative. Arithmetic mean, median, harmonic mean in suitable nonzero data, and mode can be negative.
Correct answer: Geometric Mean158. If any of the value in data set is zero then it is not possible (i.e. impossiblE. to compute_______________?
- A. Mode
- B. Median
- C. Mean
- D. Harmonic Mean
- E. Geometric Mean
Explanation: The harmonic mean is n divided by the sum of reciprocals, and a zero observation contributes 1/0, making the calculation undefined. A geometric mean may instead be zero when the data are nonnegative and include zero.
Correct answer: Harmonic Mean159. 2nd Quartile = 5th Decile = 50th Percentile = ?
- A. Mode
- B. Median
- C. Mean
- D. Geometric Mean
- E. Harmonic Mean
Explanation: Quartiles, deciles and percentiles use different scales: Q2, D5 and P50 all mark the middle observation of an ordered dataset, which is the median.
Correct answer: Median160. _____________is the measure of average which can have more than one value?
- A. Mean
- B. Median
- C. Harmonic Mean
- D. Mode
- E. Geometric Mean
Explanation: The mode is the most frequent value, and a dataset may have two or more values tied for the highest frequency, making it bimodal or multimodal. The mean and median have one value for a given dataset.
Correct answer: Mode