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Class 10 Mode of Grouped Data — practice questions with answers

Statistics and Probability · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. The class with the highest frequency in a frequency distribution is called the:
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Answer: A) Modal class
The class interval having the maximum frequency is called the modal class. The mode lies in this class.
2. In the mode formula the denominator is (2f1 - f0 - f2). For f1 = 25, f0 = 16, f2 = 12, this denominator equals:
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Answer: C) 22
2f1 - f0 - f2 = 2*25 - 16 - 12 = 50 - 28 = 22.
3. For classes 100-120, 120-140, 140-160 with frequencies 12, 30, 18, find the value of (2f1 - f0 - f2) for the modal class.
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Answer: B) 30
Modal class is 120-140 (f1=30). f0=12, f2=18. 2f1-f0-f2 = 60-12-18 = 30.
4. Electricity bills (in Rs) of 100 houses in Bhopal: 0-200 (12), 200-400 (24), 400-600 (36), 600-800 (20), 800-1000 (8).
The modal class is 400-600. Calculate the mode of the bills.
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Answer: A) 485.71
l=400, f1=36, f0=24, f2=20, h=200. Mode = 400 + *200 = 400 + *200 = 400 + 85.71 = 485.71.
5. The monthly incomes (in Rs thousands) of 150 families in a Delhi locality give a modal class 30-40 with l = 30, f1 = 50, f0 = 35, f2 = 25, h = 10. A newspaper rounds the mode to the nearest thousand rupees.
What modal income (in Rs thousands) will it report?
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Answer: D) 34
Mode = 30 + *10 = 30 + *10 = 30 + 3.75 = 33.75, which rounds to 34 (thousand rupees).
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