1. Which of the following is NOT a measure of central tendency?
A. Mean
B. Range
C. Median
D. Mode
Answer: B. Range
Explanation: The range is a measure of dispersion (spread), not central tendency. Mean, median, and mode describe the center of a data set.
2. The arithmetic mean is defined as:
A. The value that occurs most frequently
B. The middle value in an ordered data set
C. The sum of values divided by the number of values
D. The average of highest and lowest values
Answer: C. The sum of values divided by the number of values
Explanation: The mean is calculated by dividing the sum of observations by the total number of observations.
3. The median of the data set {3, 8, 2, 7, 5} is:
A. 5
B. 7
C. 3
D. 8
Answer: A. 5
Explanation: Arrange the data: 2, 3, 5, 7, 8. The middle value is 5, hence the median.
4. The mode of the data: {2, 3, 4, 3, 5, 3, 6} is:
A. 4
B. 3
C. 5
D. 6
Answer: B. 3
Explanation: The number 3 appears three times, more than any other value.
5. When a distribution has two modes, it is called:
A. Bimodal
B. Trimodal
C. Multimodal
D. Uniform
Answer: A. Bimodal
Explanation: A bimodal distribution has two modes, i.e., two values with the same highest frequency.
6. Which measure of central tendency is not affected by extreme values?
A. Mean
B. Median
C. Mode
D. Both B and C
Answer: D. Both B and C
Explanation: Median and mode are not influenced by outliers. The mean is highly affected by extreme values.
7. For a perfectly symmetrical distribution, the mean, median, and mode are:
A. All different
B. All equal
C. Two are equal
D. Cannot say
Answer: B. All equal
Explanation: In a symmetrical (normal) distribution, mean = median = mode.
8. The measure of central tendency that can be used for qualitative data is:
A. Mean
B. Median
C. Mode
D. All of these
Answer: C. Mode
Explanation: Mode can be used for categorical data (e.g., most preferred color). Mean and median require numerical data.
9. The mean of 5 numbers is 12. What is their total sum?
A. 60
B. 24
C. 120
D. 100
Answer: A. 60
Explanation: Mean = Total / N → 12 = Total / 5 → Total = 12 × 5 = 60
10. Which measure of central tendency is used in calculating GPA?
A. Mode
B. Median
C. Mean
D. Range
Answer: C. Mean
Explanation: GPA is the weighted mean of grade points.
11. The most appropriate measure of central tendency for skewed data is:
A. Mean
B. Mode
C. Median
D. Range
Answer: C. Median
Explanation: Median is less influenced by extreme values, hence preferred in skewed distributions.
12. If the mode = 20, median = 25, what is the approximate mean using the empirical formula?
A. 25
B. 30
C. 27.5
D. 32
Answer: B. 30
Explanation: Empirical relation:
Mean – Mode = 3 (Mean – Median)
⇒ Mean – 20 = 3 (Mean – 25)
⇒ Mean = 30
13. In grouped data, the modal class is the class with:
A. Maximum frequency
B. Lowest lower limit
C. Highest cumulative frequency
D. Lowest frequency
Answer: A. Maximum frequency
Explanation: Modal class is the class interval with the highest frequency.
14. Which measure of central tendency is easiest to compute from an unorganized data set?
A. Mean
B. Median
C. Mode
D. Percentile
Answer: C. Mode
Explanation: Mode can be identified just by finding the most frequent value, no need to sort or calculate.
15. In a distribution, if mean > median > mode, the distribution is:
A. Symmetrical
B. Positively skewed
C. Negatively skewed
D. Uniform
Answer: B. Positively skewed
Explanation: In positively skewed data, the tail is on the right. So, Mean > Median > Mode.
16. The sum of deviations from the mean is always:
A. Maximum
B. Minimum
C. Zero
D. Negative
Answer: C. Zero
Explanation: The algebraic sum of deviations from the mean is always zero.
17. Which measure of central tendency is most suitable for open-ended class intervals?
A. Mean
B. Mode
C. Median
D. All of the above
Answer: C. Median
Explanation: Median does not require precise class limits, making it ideal for open-ended distributions.
18. A student scored the following in 5 subjects: 50, 60, 70, 80, 100. What is the median score?
A. 60
B. 70
C. 80
D. 100
Answer: B. 70
Explanation: The data is already arranged. The middle value (3rd) is 70, so it’s the median.
19. If a student scores: 80, 90, 85, 75, 70, what is the mean score?
A. 80
B. 85
C. 82
D. 72
Answer: A. 80
Explanation:
Mean = (80 + 90 + 85 + 75 + 70) ÷ 5 = 400 ÷ 5 = 80
20. The most appropriate measure of central tendency for ordinal data is:
A. Mean
B. Mode
C. Median
D. All of the above
Answer: C. Median
Explanation: Median is suitable for ordinal data (ranked data), where the relative position matters but not the distance.
21. Which measure of central tendency can be used for nominal data (e.g., gender, religion)?
A. Mean
B. Median
C. Mode
D. None
Answer: C. Mode
Explanation: Only mode can be used with nominal/categorical data, identifying the most frequent category.
22. If in a dataset, mean = 60 and median = 65, the distribution is likely:
A. Symmetrical
B. Positively skewed
C. Negatively skewed
D. Normal
Answer: C. Negatively skewed
Explanation: In negatively skewed distributions: mean < median < mode
23. Which is the most stable measure of central tendency?
A. Mean
B. Median
C. Mode
D. All are equally stable
Answer: A. Mean
Explanation: The mean is mathematically precise and uses all values, making it most stable for statistical analysis.
24. Which of the following is affected most by extreme values?
A. Mean
B. Median
C. Mode
D. None
Answer: A. Mean
Explanation: Extreme values (outliers) directly change the mean since it includes all values in calculation.
25. If the data has no repeated value, the mode is:
A. Zero
B. Cannot be calculated
C. Not defined
D. Mean
Answer: C. Not defined
Explanation: Mode is the most frequent value. If all values are unique, mode is not defined.
26. When should the median be preferred over the mean?
A. In normal distribution
B. In symmetric data
C. In data with outliers
D. In small data sets
Answer: C. In data with outliers
Explanation: Median is not influenced by outliers, making it suitable for skewed or extreme data.
27. The geometric mean is suitable for:
A. Skewed distributions
B. Rates and ratios
C. Categorical data
D. Nominal data
Answer: B. Rates and ratios
Explanation: Geometric mean is appropriate when data involve percentages, indices, or multiplicative rates (e.g., growth rates).
28. The empirical relationship between mean, median, and mode is:
A. Mode = 3 Median – 2 Mean
B. Mode = 2 Median – Mean
C. Mean = 3 Mode – 2 Median
D. Mean = Mode + Median
Answer: A. Mode = 3 Median – 2 Mean
Explanation: This is Karl Pearson’s empirical formula for moderately skewed distributions.
29. In a frequency distribution, the median class is located by:
A. Locating the highest frequency
B. Finding where N/2N/2 lies
C. Finding the mean
D. Adding the mode to the class interval
Answer: B. Finding where N/2N/2 lies
Explanation: The median class is the class whose cumulative frequency ≥ N/2.
30. The best measure for qualitative variables is:
A. Mean
B. Median
C. Mode
D. Standard deviation
Answer: C. Mode
Explanation: Only mode is meaningful for qualitative variables (e.g., most preferred brand or choice).
31. Which central tendency is least used in scientific research due to its unreliability?
A. Mean
B. Median
C. Mode
D. Harmonic mean
Answer: C. Mode
Explanation: Mode is less consistent, especially in data with multiple modes or no repeated value.
32. If a distribution is symmetrical, then:
A. Mean = Median = Mode
B. Mean > Median > Mode
C. Mode > Median > Mean
D. Mean < Median = Mode
Answer: A. Mean = Median = Mode
Explanation: In perfectly symmetrical distributions, all three measures coincide.
33. If a class interval is 20–30 with frequency 15, and the median lies in this class, what is the class width (h)?
A. 5
B. 10
C. 15
D. 20
Answer: B. 10
Explanation: Class width = 30 – 20 = 10
34. The average of the lower and upper quartiles is called:
A. Mode
B. Median
C. Mid-quartile
D. Decile
Answer: C. Mid-quartile
Explanation: Mid-quartile = Q1+Q32\frac{Q1 + Q3}{2}, an average of the 1st and 3rd quartiles.
35. The harmonic mean is useful for:
A. Speed and rate problems
B. Skewed data
C. Ordinal data
D. Categorical data
Answer: A. Speed and rate problems
Explanation: Harmonic mean is used when the data is in the form of rates, like speed (distance/time).
36. If the scores are 3, 3, 4, 5, 6, 7, 8, then the median is:
A. 5
B. 6
C. 4
D. 7
Answer: A. 5
Explanation: There are 7 values → middle one (4th) = 5
37. In a data set where mean < median, the distribution is:
A. Symmetrical
B. Positively skewed
C. Negatively skewed
D. Uniform
Answer: C. Negatively skewed
Explanation: When mean < median, the tail is on the left, indicating a negative skew.