Measures of central tendency mean median and mode for grouped and ungrouped data - Question Bank

1. The median of the ungrouped data set: 5, 8, 12, 15, 20 is:
A) 8
B) 12
C) 10
D) 15
2. Which measure of central tendency is often used for discrete data where the most common category is important?
A) Mean
B) Median
C) Mode
D) Variance
3. If a dataset consists of only one value, what are its mean, median, and mode?
A) Undefined
B) Zero
C) The value itself
D) Cannot be determined
4. What is the mean of the ungrouped data set: 1, 2, 3, 4, 5, 6?
A) 3
B) 3.5
C) 4
D) 4.5
5. For a grouped frequency distribution, the mode can be approximated by the formula: L + [(f1 - f0) / (2f1 - f0 - f2)] * h. Here, f1 represents:
A) The frequency of the class preceding the modal class.
B) The frequency of the modal class.
C) The frequency of the class succeeding the modal class.
D) The cumulative frequency of the modal class.
6. Which of the following is NOT a measure of central tendency?
A) Mean
B) Median
C) Mode
D) Range
7. What is the median of the ungrouped data set: 10, 12, 14, 16, 18, 20?
A) 14
B) 15
C) 16
D) 17
8. In calculating the mean of grouped data using the assumed mean method, deviations are taken from:
A) The actual mean
B) The median
C) An assumed mean
D) The mode
9. Which measure of central tendency is a positional average?
A) Mean
B) Median
C) Mode
D) Variance
10. If a dataset has two modes, it is called:
A) Unimodal
B) Bimodal
C) Multimodal
D) Amadal
11. What is the mean of the ungrouped data set: 5, 10, 15?
A) 5
B) 10
C) 15
D) 20
12. Which measure is best suited when the data contains extreme values or outliers?
A) Mean
B) Median
C) Mode
D) Standard Deviation
13. For the grouped data, if the lower limit of the median class is 50, N/2 is 60, the cumulative frequency of the preceding class is 45, and the frequency of the median class is 30, what is the median?
A) 50
B) 55
C) 58.33
D) 60
14. If the mean of a dataset is 30 and the median is 35, the distribution is likely:
A) Symmetrical
B) Positively skewed
C) Negatively skewed
D) Uniform
15. What is the median of the ungrouped data set: 15, 25, 35, 45, 55, 65?
A) 35
B) 40
C) 45
D) 50
16. Which measure of central tendency is calculated using all the values in a dataset?
A) Median
B) Mode
C) Mean
D) Quartile Deviation
17. The median of a grouped frequency distribution requires knowledge of the:
A) Modal class
B) Mean class
C) Median class
D) Class with highest frequency
18. If a dataset has no repeating values, what is its mode?
A) 0
B) 1
C) The mean
D) It has no mode
19. What is the mode of the ungrouped data set: 1, 2, 2, 3, 3, 4, 4, 4, 5?
A) 2
B) 3
C) 4
D) 5
20. In a grouped data set, if N=100 and the cumulative frequency just before the median class is 40, and the frequency of the median class is 20, what is N/2 - CF?
A) 10
B) 20
C) 30
D) 40
21. Which measure of central tendency is most suitable for ordinal data?
A) Mean
B) Median
C) Mode
D) Geometric Mean
22. What is the mean of the ungrouped data set: 2, 4, 6, 8?
A) 4
B) 5
C) 6
D) 10
23. If the mean of a dataset is 25 and the median is 22, the distribution is likely:
A) Symmetrical
B) Positively skewed
C) Negatively skewed
D) Bimodal
24. The modal class for a grouped frequency distribution is the class with:
A) The highest cumulative frequency.
B) The lowest frequency.
C) The highest frequency.
D) The largest range.
25. What is the median of the ungrouped data set: 7, 1, 5, 3, 9?
A) 1
B) 3
C) 5
D) 7
26. For a negatively skewed distribution (left-skewed), the relationship between mean, median, and mode is typically:
A) Mean < Median < Mode
B) Mean > Median > Mode
C) Mean = Median = Mode
D) Mode < Median < Mean
27. Which of the following is a disadvantage of using the mean?
A) It is affected by extreme values.
B) It cannot be calculated for grouped data easily.
C) It is not a unique value.
D) It is not affected by outliers.
28. A dataset has values: 5, 5, 5, 5. What is its mode?
A) 0
B) 1
C) 5
D) Undefined
29. What is the median of the ungrouped data set: 1, 1, 2, 3, 3, 3, 4, 5?
A) 2.5
B) 3
C) 3.5
D) 4
30. For grouped data, the class mark of a class interval is calculated as:
A) (Lower limit + Upper limit) / 2
B) Upper limit - Lower limit
C) Lower limit / Frequency
D) Upper limit * Frequency
31. What is the mean of the ungrouped data set: 10, 20, 30, 40, 50?
A) 20
B) 30
C) 40
D) 50
32. Consider the ungrouped data: 1, 2, 3, 4, 5, 100. Which measure would be most representative of the central tendency?
A) Mean
B) Median
C) Mode
D) All are equally representative
33. Which measure of central tendency is most appropriate for nominal data?
A) Mean
B) Median
C) Mode
D) Range
34. The empirical relation for a moderately skewed distribution is often given as: Mean - Mode = 3 * (Mean - Median). This can be rearranged to find the Mode if Mean and Median are known. What is the Mode if Mean = 50 and Median = 45?
A) 40
B) 45
C) 50
D) 55
35. In a grouped frequency distribution, the mode is often estimated using:
A) The midpoint of the modal class.
B) The lower limit of the modal class.
C) An empirical relation involving mean and median.
D) The class mark of the class with the highest cumulative frequency.
36. What does 'N' represent in the median formula for grouped data?
A) The number of classes.
B) The total frequency (sum of all frequencies).
C) The upper limit of the median class.
D) The cumulative frequency of the median class.
37. The formula for calculating the median of a grouped frequency distribution is L + [(N/2 - CF) / f] * h, where L is:
A) The upper boundary of the median class.
B) The lower boundary of the median class.
C) The class mark of the median class.
D) The frequency of the median class.
38. If all values in an ungrouped data set are the same, what is the mean, median, and mode?
A) Undefined
B) Zero
C) The common value
D) Cannot be determined
39. What is the median of the ungrouped data set: 10, 20, 30, 40?
A) 20
B) 25
C) 30
D) 35
40. Which measure of central tendency is least affected by outliers in a dataset?
A) Mean
B) Median
C) Mode
D) Variance
41. For a positively skewed distribution (right-skewed), the relationship between mean, median, and mode is typically:
A) Mean < Median < Mode
B) Mean > Median > Mode
C) Mean = Median = Mode
D) Median < Mode < Mean
42. The formula for calculating the mean of a grouped frequency distribution is:
A) Sum of (frequency * class mark) / Sum of frequencies
B) Sum of (frequency * lower limit) / Sum of frequencies
C) Sum of (frequency * upper limit) / Sum of frequencies
D) Sum of class marks / Number of classes
43. In a grouped frequency distribution, how is the median class determined?
A) The class with the highest frequency.
B) The class where the cumulative frequency exceeds N/2.
C) The class with the smallest lower limit.
D) The class with the largest upper limit.
44. What is the mode of the ungrouped data set: 3, 4, 4, 5, 6, 6, 6, 7?
A) 4
B) 5
C) 6
D) 7
45. For a symmetrical distribution of ungrouped data, which of the following is generally true?
A) Mean > Median > Mode
B) Mean < Median < Mode
C) Mean = Median = Mode
D) Mean = Mode and Median is different
46. Which measure of central tendency is calculated by summing all values and dividing by the number of values?
A) Median
B) Mode
C) Mean
D) Range
47. If a dataset has multiple values that appear with the highest frequency, how many modes can it have?
A) One
B) Two
C) Three
D) More than one
48. What is the median of the ungrouped data set: 2, 5, 8, 10, 12?
A) 5
B) 8
C) 7
D) 10
49. Which measure of central tendency represents the most frequent value in a dataset?
A) Mean
B) Median
C) Mode
D) Standard Deviation
50. For a given set of ungrouped data, which measure of central tendency is most affected by extreme values?
A) Median
B) Mean
C) Mode
D) Geometric Mean
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