1. For grouped data: class 0–10 (f=4), 10–20 (f=6), 20–30 (f=10). Find mean (direct method).
- A15
- B18
- C20
- D16
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Answer: B) 18
Marks 5, 15, 25. Σfx = 20+90+250 = 360. Σf = 20. Mean = 18.
Class 10 Statistics — 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.
2. If the mean of a distribution is 28 and the median is 30, find the mode using the empirical relation.
- A34
- B37
- C31
- D68
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Answer: A) 34
Mode = 3 Median − 2 Mean = 3(30) − 2(28) = 90 − 56 = 34.
3. The mean of the following data is 18. Class 11–13:3, 13–15:6, 15–17:9, 17–19:13, 19–21:f, 21–23:5, 23–25:4. Using mean = 18, the missing frequency f is ____.
- A8
- B16
- C9
- D7
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Answer: A) 8
Marks 12,14,16,18,20,22,24. Σf = 40+f. Σfx = 36+84+144+234+20f+110+96 = 704+20f. Mean: (704+20f)/(40+f)=18 → 704+20f = 720+18f → 2f = 16 → f = 8.
4. The modal class of a distribution turns out to be the very first class of the table. In the mode formula, what should be done about f₀?
- ATake f₀ equal to f₁, since there is no class before it
- BTreat the second class as the modal class instead
- CTake f₀ = 0, since there is no class before the modal class
- DThe mode cannot be calculated in this situation
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Answer: C) Take f₀ = 0, since there is no class before the modal class
f₀ is the frequency of the class immediately before the modal class. If no such class exists then no observations lie there, so f₀ = 0 and the formula still works, becoming Mode = l + h·f₁/(2f₁ − f₂).
5. Continuing with that data (n = 72, median class 20–30, l = 20, cf = 30, f = 16, h = 10), the median is ____.
- A20.38
- B22.50
- C25.00
- D23.75
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Answer: D) 23.75
Median = 20 + 10 × (36 − 30)/16 = 20 + 60/16 = 20 + 3.75 = 23.75. (20.38 is the result of omitting h = 10 from the formula.)
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