1. In a histogram, a class of width 10 has frequency density 2.5. Its frequency is:
- 4
- 25
- 12.5
- 0.25
Answer: B) 25
Explanation: Frequency = density width = 2.5 10 = 25. SLO M-09-C-01 · Knowledge
MCQs / Mathematics / Frequency Distribution
Frequency Distribution MCQs — Mathematics
23 multiple-choice questions on Frequency Distribution from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.
2. Marks Students ------ 0–9 3 10–19 7 20–29 12 30–39 8 How many students scored 20 or more?
- 12
- 22
- 8
- 20
Answer: D) 20
Explanation: 12 + 8 = 20. SLO M-09-C-01 · Knowledge
3. The midpoint (class mark) of the class 20 –29 is:
- 9
- 24.5
- 49
- 25.5
Answer: B) 24.5
Explanation: Midpoint = 20 + 292 = 24.5. SLO M-09-C-01 · Knowledge
4. In a histogram, the area of each bar represents:
- the cumulative frequency
- the midpoint
- the class width
- the frequency of the class
Answer: D) the frequency of the class
Explanation: Area = width density = frequency. SLO M-09-C-01 · Knowledge
5. When class intervals are unequal, the bars of a histogram should have heights equal to:
- the cumulative frequency
- the frequency
- the class width
- frequency ÷ class width
Answer: D) frequency ÷ class width
Explanation: Using frequency density makes the area of each bar proportional to its frequency. SLO M-09-C-01 · Knowledge
6. The class width (class interval) of 10 –19 (whole numbers) is:
- 10
- 9
- 29
- 4
Answer: A) 10
Explanation: Width = (19 + 0.5) - (10 - 0.5) = 10. SLO M-09-C-01 · Knowledge
7. A frequency polygon is closed by joining the ends to the horizontal axis at:
- the midpoints of the empty classes before the first and after the last class
- the origin
- the highest frequency
- the class boundaries of the first class
Answer: A) the midpoints of the empty classes before the first and after the last class
Explanation: This keeps the area under the polygon equal to that of the histogram. SLO M-09-C-01 · Knowledge
8. In a histogram with unequal class widths, a class of width 5 has frequency 15. The height of its bar (frequency density) is:
- 75
- 3
- 15
- 0.33
Answer: B) 3
Explanation: Frequency density = frequency class width = 155 = 3. SLO M-09-C-01 · Knowledge
9. The data range from 5 to 64. Using a class width of 6, the number of classes needed is:
- 59
- 12
- 8
- 10
Answer: D) 10
Explanation: The values 5 to 64 cover 64 - 5 + 1 = 60 whole numbers; 606 = 10, rounded up to 10 classes. SLO M-09-C-01 · Knowledge
10. In a histogram with unequal class widths, a class of width 4 has frequency 12. The height of its bar (frequency density) is:
- 48
- 3
- 12
- 0.33
Answer: B) 3
Explanation: Frequency density = frequency class width = 124 = 3. SLO M-09-C-01 · Knowledge
11. To draw a frequency polygon, we plot each frequency against the:
- upper class boundary
- class midpoint
- cumulative frequency
- lower class limit
Answer: B) class midpoint
Explanation: The points (midpoint, frequency) are joined with straight lines. SLO M-09-C-01 · Knowledge
12. For the class 21 –25 (whole-number data), the class boundaries are:
- 20.5 and 25.5
- 20 and 26
- 21.5 and 24.5
- 21 and 25
Answer: A) 20.5 and 25.5
Explanation: Subtract 0.5 from the lower limit and add 0.5 to the upper limit: 20.5 and 25.5. SLO M-09-C-01 · Knowledge
13. A grouped frequency table is most useful when:
- every value occurs once only
- there are only three values
- the data are names
- there are many different data values
Answer: D) there are many different data values
Explanation: Grouping summarises large data sets. SLO M-09-C-01 · Knowledge
14. In a histogram with unequal class widths, a class of width 8 has frequency 24. The height of its bar (frequency density) is:
- 192
- 3
- 24
- 0.33
Answer: B) 3
Explanation: Frequency density = frequency class width = 248 = 3. SLO M-09-C-01 · Knowledge
15. In a histogram with unequal class widths, a class of width 20 has frequency 30. The height of its bar (frequency density) is:
- 600
- 1.5
- 0.67
- 30
Answer: B) 1.5
Explanation: Frequency density = frequency class width = 3020 = 1.5. SLO M-09-C-01 · Knowledge
16. The class width (class interval) of 35 –49 (whole numbers) is:
- 7
- 84
- 14
- 15
Answer: D) 15
Explanation: Width = (49 + 0.5) - (35 - 0.5) = 15. SLO M-09-C-01 · Knowledge
17. The midpoint (class mark) of the class 45 –54 is:
- 49.5
- 50.5
- 9
- 99
Answer: A) 49.5
Explanation: Midpoint = 45 + 542 = 49.5. SLO M-09-C-01 · Knowledge
18. The midpoint (class mark) of the class 0 –4 is:
- 4
- 2
- 1
- 3
Answer: B) 2
Explanation: Midpoint = 0 + 42 = 2. SLO M-09-C-01 · Knowledge
19. Marks Students ------ 0–9 3 10–19 7 20–29 12 30–39 8 The cumulative frequency up to the class 20–29 is:
- 22
- 10
- 30
- 12
Answer: A) 22
Explanation: 3 + 7 + 12 = 22. SLO M-09-C-01 · Knowledge
20. For the class 10 –19 (whole-number data), the class boundaries are:
- 9.5 and 19.5
- 9 and 20
- 10 and 19
- 10.5 and 18.5
Answer: A) 9.5 and 19.5
Explanation: Subtract 0.5 from the lower limit and add 0.5 to the upper limit: 9.5 and 19.5. SLO M-09-C-01 · Knowledge
21. For the class 100 –119 (whole-number data), the class boundaries are:
- 100.5 and 118.5
- 100 and 119
- 99.5 and 119.5
- 99 and 120
Answer: C) 99.5 and 119.5
Explanation: Subtract 0.5 from the lower limit and add 0.5 to the upper limit: 99.5 and 119.5. SLO M-09-C-01 · Knowledge
22. Unlike a bar chart, the bars of a histogram for continuous data:
- always have gaps between them
- touch each other with no gaps
- are always the same height
- are drawn horizontally
Answer: B) touch each other with no gaps
Explanation: The class boundaries join up, so the bars are adjacent. SLO M-09-C-01 · Knowledge
23. The data range from 12 to 87. Using a class width of 10, the number of classes needed is:
- 75
- 10
- 6
- 8
Answer: D) 8
Explanation: The values 12 to 87 cover 87 - 12 + 1 = 76 whole numbers; 7610 = 7.6, rounded up to 8 classes. SLO M-09-C-01 · Knowledge
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