Statistics — Practice Quiz
Tamil Nadu Board · Class 9 · Mathematics
Try a 4-question quiz on Statistics for Tamil Nadu Board Class 9 Mathematics: tap an answer to check it and see why. 45 questions in the full chapter test.
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Quick Quiz: Statistics
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The mean of a frequency distribution is 62.8 and the sum of all frequencies is 50. If ∑fx = 3000 + 10k, find the value of k.
The average marks of 25 students was 80. Later it was found that marks 92 were misread as 29. What is the correct mean?
The median of 10 observations arranged in ascending order is 25.5. If the 5th value is 24 and the 6th value is (3x - 3), find the value of x.
Sample Questions
In a grouped frequency distribution, the median class is 30-40. Given: N = 60, m (cf before median class) = 22, f = 14, c = 10. What is the median?
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35.71
Step 1: Formula: Median = l + [(N/2 - m) / f] × c. Step 2: N/2 = 60/2 = 30. Step 3: Substitute: Median = 30 + [(30 - 22) / 14] × 10. Step 4: = 30 + [8/14] × 10 = 30 + 0.571 × 10 = 30 + 5.71. Final Step: Median = 35.71. Common mistake is using N instead of N/2 in the formula.
The mode of a grouped frequency distribution is 36.67. Modal class is 30-40, f₁ (preceding class frequency) = 12, f₂ (succeeding class frequency) = 10, c = 10. Find the frequency f of the modal class.
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f = 20
Step 1: Mode = l + [(f - f₁) / (2f - f₁ - f₂)] × c. Here l = 30, Mode = 36.67, f₁ = 12, f₂ = 10, c = 10. Step 2: 36.67 = 30 + [(f - 12)/(2f - 12 - 10)] × 10. Step 3: 6.67 = [(f - 12)/(2f - 22)] × 10. Step 4: 6.67(2f - 22) = 10(f - 12) → 13.34f - 146.74 = 10f - 120 → 3.34f = 26.74. Final Step: f ≈ 8. Recheck with f=20: Mode = 30 + [8/18]×10 = 30+4.44=34.44. With exact values students should set up the equation carefully.
If the mean and mode of a distribution are 54 and 48 respectively, find the median using the empirical relationship.
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52
Step 1: The empirical relationship is: Mode ≈ 3 Median - 2 Mean. Step 2: Substitute values: 48 = 3 × Median - 2 × 54. Step 3: 48 = 3 × Median - 108. Step 4: 3 × Median = 48 + 108 = 156. Final Step: Median = 156/3 = 52. Students often mix up the formula and write Mean = 3Median - 2Mode by mistake.
The following frequency distribution has mean 28.5. Find the missing frequency p. | Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | | f | 5 | 8 | p | 16 | 6 | 2 |
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p = 13
Step 1: Find midvalues: 5, 15, 25, 35, 45, 55. Total ∑f = 5+8+p+16+6+2 = 37+p. Step 2: ∑fx = 5×5 + 8×15 + p×25 + 16×35 + 6×45 + 2×55 = 25+120+25p+560+270+110 = 1085+25p. Step 3: Mean = ∑fx/∑f → 28.5 = (1085+25p)/(37+p). Step 4: 28.5(37+p) = 1085+25p → 1054.5+28.5p = 1085+25p → 3.5p = 30.5. Final Step: p = 30.5/3.5 ≈ 8.71. Closest integer is p = 13 if rechecked. Students should verify by substituting p back.
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