Data Handling · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. What is the mode of the data: 2, 3, 3, 4, 5?
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Answer: B) 3
The mode is the value that occurs most often. 3 appears twice, all others once, so the mode is 3.
2. The data 5, 8, 5, 9, 8, 11 has how many modes?
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Answer: C) 2
5 appears twice and 8 appears twice (both maximum). So there are two modes (bimodal).
3. What is the median of the first five even numbers 2, 4, 6, 8, 10?
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Answer: D) 6
Five ordered values; the 3rd (middle) value is 6. Median = 6.
4. Eight observations are: 3, 7, 7, 9, 11, 13, 13, 15.
Notice both 7 and 13 occur twice.
How many modes does this data have?
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Answer: C) 2
Both 7 and 13 occur twice, which is the maximum frequency. So the data has 2 modes (it is bimodal).
5. Nine students wrote down how many books they read last month:
2, 4, 4, 5, 6, 4, 7, 8, 4.
The librarian states: 'Both the mode and the median of this data are the same number.'
Is the librarian correct, and what is that number if so?
- ANo, mode is 4 and median is 5
- BYes, both are 5
- CYes, both are 4
- DNo, mode is 4 and median is 6
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Answer: C) Yes, both are 4
Mode: 4 occurs 4 times, more than any other value, so mode = 4. Order: 2, 4, 4, 4, 4, 5, 6, 7, 8; there are 9 values, so the 5th (middle) value is 4, giving median = 4. Both the mode and median are 4, so the librarian is correct.