Statistics — Important Questions
Tamil Nadu Board · Class 9 · Mathematics
45 important questions from Statistics for Tamil Nadu Board Class 9 Mathematics, with answers. Includes multiple choice questions.
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Important Questions from Statistics
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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