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Statistics

Tamil Nadu Board · Class 9 · Mathematics

Practice quiz for Statistics — Tamil Nadu Board Class 9 Mathematics. MCQs and questions with answers to test your preparation.

45 questions25 flashcards5 concepts

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Quick Quiz: Statistics

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1

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.

2

Using the Step Deviation Method with assumed mean A = 25 and class width c = 10, if ∑f = 40 and ∑fd = -12, what is the arithmetic mean?

3

The average marks of 25 students was 80. Later it was found that marks 92 were misread as 29. What is the correct mean?

4

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.

45 Questions·
multiple choice

Sample Questions

1multiple choice
1 marks

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?

Show answer

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.

2multiple choice
1 marks

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.

Show answer

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.

3multiple choice
1 marks

If the mean and mode of a distribution are 54 and 48 respectively, find the median using the empirical relationship.

Show answer

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.

4multiple choice
1 marks

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 |

Show answer

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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Frequently Asked Questions

What are the important topics in Statistics for Tamil Nadu Board Class 9 Mathematics?
Key topics in Statistics include Statistics Chapter Overview Mind Map, Statistics Chapter - Complete Concept Map, Mind map showing the types of data collection methods and their categories. These are the concepts Tamil Nadu Board Class 9 examiners draw on most — study them first, then practise related questions.
How to score full marks in Statistics — Tamil Nadu Board Class 9 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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