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 20 of 55
191. The sum of squared deviations of a set of n values from their mean is__________________?
- A. Zero
- B. Maximum
- C. Least
- D. None
Explanation: The arithmetic mean is the value that minimizes the sum of squared deviations. Thus, deviations squared from the mean have the least possible sum, not necessarily a zero sum.
Correct answer: Least192. The measure of dispersion is changed by a change of_____________?
- A. Origin
- B. Scale
- C. Algebraic Signs
- D. None
Explanation: Changing the origin adds or subtracts a constant and leaves spread unchanged, but changing the scale multiplies dispersion measures. Therefore, dispersion is affected by a change of scale.
Correct answer: Scale193. The algebraic sum of deviations from mean is_____________?
- A. Maximum
- B. Zero
- C. Minimum
- D. Undefined
Explanation: Positive and negative deviations from the arithmetic mean balance each other exactly. Therefore, their algebraic sum is zero.
Correct answer: Zero194. You asked five of your classmates about their height. On the basis of this information, you stated that the average height of all students in your university or college is 67 inches. This is an example of ?
- A. Descriptive statistics
- B. Inferential Statistics
- C. Parameter
- D. Population
Explanation: The five classmates form a sample, and the statement extends their average height to all university or college students. Drawing a conclusion about a population from sample information is inferential statistics.
Correct answer: Inferential Statistics195. Which one of the following measurement does not divide a set of observations into equal parts ?
- A. Quartiles
- B. Standard Deviations
- C. Percentiles
- D. Deciles
- E. Median
Explanation: Quartiles, deciles, percentiles, and the median are positional measures that divide ordered data into specified parts. Standard deviation measures spread and does not divide observations into equal groups.
Correct answer: Standard Deviations196. Which of the following is not based on all the observations ?
- A. Arithmetic Mean
- B. Geometric Mean
- C. Harmonic Mean
- D. Weighted Mean
- E. Mode
Explanation: The mode is determined by the most frequent value, so it does not require every observation in the calculation. Means use the values, and a weighted mean also uses the observations with assigned weights.
Correct answer: Mode197. The height of a student is 60 inches. This is an example of________________?
- A. Qualitative data
- B. Categorical data
- C. Continuous data
- D. Discrete data
Explanation: Height is continuous because it can take any value within a range, including fractional inches such as 60.2 or 60.25. Recording it as 60 does not change the nature of the measurement.
Correct answer: Continuous data198. Which of these is a relative measure of dispersion_____________?
- A. Standard Deviation
- B. Variance
- C. Coefficient of Variation
- D. None of these
Explanation: The coefficient of variation is relative because it expresses standard deviation in relation to the mean, usually as a percentage. Standard deviation and variance are absolute measures of dispersion.
Correct answer: Coefficient of Variation199. Which one is the not measure of dispersion?
- A. The Range
- B. 50th Percentile
- C. Inter-Quartile Range
- D. Variance
Explanation: The 50th percentile is the median, a measure of central tendency rather than dispersion. Range, interquartile range, and variance all describe spread in the data.
Correct answer: 50th Percentile200. In statistics, conducting a survey means_____________?
- A. Collecting information from elements
- B. Making mathematical calculations
- C. Drawing graphs and pictures
- D. None of the above
Explanation: Conducting a survey involves collecting information from selected elements or respondents according to a planned method. Calculations and graphs are later stages of analysing or presenting the collected information.
Correct answer: Collecting information from elements