Measures of Central Tendency and Dispersion - Question Bank

1. The median of a dataset with an even number of observations is the:
A) Average of the two middle observations
B) First middle observation
C) Second middle observation
D) Average of all observations
2. Which measure of central tendency is represented by the peak of a frequency distribution curve?
A) Mean
B) Median
C) Mode
D) Range
3. What is the mean of the dataset: 10, 10, 10, 10, 10?
A) 0
B) 10
C) 50
D) 100
4. For a dataset with values 5, 10, 15, 20, 25, what is Q3?
A) 10
B) 15
C) 20
D) 25
5. For a dataset with values 5, 10, 15, 20, 25, what is Q1?
A) 5
B) 10
C) 15
D) 20
6. Which measure of dispersion is calculated as (Q3 - Q1) / 2?
A) Range
B) Interquartile Range
C) Quartile Deviation
D) Standard Deviation
7. The sum of deviations from the median is minimized when the deviations are taken as:
A) Absolute deviations
B) Squared deviations
C) Deviations from the mean
D) Deviations from the mode
8. If the mean is 20 and the standard deviation is 4, what is the coefficient of variation (CV)?
A) 0.2
B) 5
C) 20
D) 80
9. The coefficient of variation is a measure of:
A) Central tendency
B) Absolute dispersion
C) Relative dispersion
D) Skewness
10. Which measure of central tendency is often used for salary data because it is less affected by very high salaries?
A) Mean
B) Median
C) Mode
D) Range
11. The sum of the first n natural numbers is n(n+1)/2. What is the mean of the first 10 natural numbers?
A) 5
B) 5.5
C) 10
D) 55
12. If the mode of a dataset is 15, it means that the value 15:
A) Is the average of the dataset
B) Occurs most frequently
C) Is the middle value
D) Is the highest value
13. What is the median of the dataset: 10, 20, 30, 40, 50, 60?
A) 30
B) 35
C) 40
D) 45
14. Which measure of dispersion is sensitive to extreme values?
A) Interquartile Range
B) Standard Deviation
C) Median Absolute Deviation
D) Quartile Deviation
15. If a dataset has a mean of 50 and a standard deviation of 0, what can be concluded?
A) The dataset has only one value
B) All values in the dataset are 50
C) The dataset is empty
D) The mean is incorrect
16. For a dataset with values 1, 3, 5, 7, 9, what is the mean of the first and last value (Midrange)?
A) 1
B) 5
C) 9
D) 10
17. The harmonic mean is most useful when dealing with:
A) Ratios and rates
B) Large numbers
C) Small numbers
D) Qualitative data
18. Which measure of central tendency is calculated by multiplying the values and taking the nth root?
A) Arithmetic Mean
B) Geometric Mean
C) Harmonic Mean
D) Median
19. The 'average of the averages' is a concept related to:
A) Median
B) Mode
C) Weighted Mean
D) Geometric Mean
20. Which of the following is NOT a measure of dispersion?
A) Range
B) Variance
C) Quartile Deviation
D) Mean
21. Which of the following is NOT a measure of central tendency?
A) Mean
B) Median
C) Mode
D) Standard Deviation
22. In a dataset, Q1 = 10 and Q3 = 25. What is the Interquartile Range?
A) 10
B) 15
C) 25
D) 35
23. Which measure of dispersion is resistant to outliers?
A) Range
B) Standard Deviation
C) Variance
D) Interquartile Range
24. If the standard deviation of a dataset is 5, what is its variance?
A) 5
B) 10
C) 25
D) 50
25. What is the variance of the dataset: 2, 2, 2, 2?
A) 0
B) 1
C) 2
D) 4
26. Consider the dataset: 1, 2, 3, 4, 5, 6. What is the median?
A) 3
B) 3.5
C) 4
D) 4.5
27. A dataset has values: 3, 5, 7, 9, 11. What is the range?
A) 5
B) 8
C) 11
D) 9
28. A dataset has values: 2, 4, 6, 8, 10. What is the mean?
A) 4
B) 5
C) 6
D) 7
29. A dataset has values: 5, 7, 7, 8, 9, 10. What is the mode?
A) 5
B) 7
C) 8
D) 9
30. A dataset has values: 10, 12, 15, 16, 17. What is the median?
A) 12
B) 15
C) 16
D) 13.6
31. The sum of squares of deviations from the mean is minimized when the deviations are calculated from the:
A) Median
B) Mode
C) Mean
D) Midrange
32. Which of the following is a measure of dispersion?
A) Mean
B) Median
C) Mode
D) Range
33. The second quartile (Q2) of a dataset is equivalent to the:
A) First quartile (Q1)
B) Third quartile (Q3)
C) Median
D) Mode
34. If a dataset is skewed to the right (positively skewed), the relationship between mean, median, and mode is typically:
A) Mean < Median < Mode
B) Mode < Median < Mean
C) Mean = Median = Mode
D) Mean > Mode > Median
35. The mean absolute deviation (MAD) is the average of the:
A) Squared deviations from the mean
B) Absolute deviations from the mean
C) Deviations from the median
D) Deviations from the mode
36. Which measure of central tendency is suitable for qualitative data?
A) Mean
B) Median
C) Mode
D) Standard Deviation
37. For a symmetric distribution, which of the following relationships generally holds true?
A) Mean < Median < Mode
B) Mode < Median < Mean
C) Mean = Median = Mode
D) Mean > Mode > Median
38. The sum of deviations of each observation from the mean is always:
A) Equal to the mean
B) Equal to the standard deviation
C) Zero
D) The variance
39. Quartiles divide a dataset into how many equal parts?
A) Two
B) Three
C) Four
D) Ten
40. The interquartile range (IQR) is the difference between the:
A) Maximum and minimum values
B) Third quartile and the first quartile
C) Mean and the median
D) Mode and the median
41. Which measure of dispersion is expressed in the same units as the original data?
A) Variance
B) Interquartile Range
C) Standard Deviation
D) Mean Absolute Deviation
42. If all values in a dataset are the same, the standard deviation is:
A) Equal to the mean
B) Equal to the median
C) Zero
D) Undefined
43. The standard deviation is the:
A) Square of the variance
B) Square root of the variance
C) Sum of squared deviations from the mean
D) Average of the absolute deviations from the mean
44. Variance is a measure of:
A) Central tendency
B) Dispersion
C) Skewness
D) Kurtosis
45. The range of a dataset is calculated as:
A) Sum of all observations
B) Highest value minus the lowest value
C) Average of the two middle values
D) Most frequent value
46. Which measure of central tendency is most affected by extreme values (outliers)?
A) Median
B) Mode
C) Mean
D) Geometric Mean
47. The mode of a dataset is the:
A) Value that occurs most frequently
B) Average of all values
C) Middle value when data is ordered
D) Difference between the highest and lowest values
48. If a dataset has an odd number of observations, the median is the:
A) First observation
B) Last observation
C) Middle observation when data is ordered
D) Average of the first and last observation
49. The arithmetic mean of a dataset is also known as the:
A) Mode
B) Median
C) Average
D) Midrange
50. Which of the following is a measure of central tendency?
A) Range
B) Variance
C) Median
D) Quartile Deviation
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