Question 9 of 21intermediate🔧 ApplyNumerical3 marks

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Literacy rate (in %)45 - 5555 - 6565 - 7575 - 8585 - 95
Number of cities3101183
Correct Answer

The mean literacy rate is 69.43%.

Exercise: EXERCISE 13.1 | Q: 9 | (Page 13)
For More Understanding

Explanation

This question is from Exercise 13.2 of the NCERT textbook, asking students to find the mean of grouped data. The direct method is used here, where we find class marks (midpoints) for each class interval, multiply them by respective frequencies, sum the products, and divide by total frequency. The calculation is straightforward and follows the standard procedure taught in the chapter.

Solution Steps

  1. Step 1: Find the class marks (xᵢ) for each class interval using the formula: Class mark = (Lower limit + Upper limit) / 2

  2. Step 2: For 45-55: x₁ = (45+55)/2 = 50; For 55-65: x₂ = (55+65)/2 = 60; For 65-75: x₃ = (65+75)/2 = 70; For 75-85: x₄ = (75+85)/2 = 80; For 85-95: x₅ = (85+95)/2 = 90

  3. Step 3: Calculate fᵢ × xᵢ for each class: 3×503 \times 50 = 150; 10×6010 \times 60 = 600; 11×7011 \times 70 = 770; 8×808 \times 80 = 640; 3×903 \times 90 = 270

  4. Step 4: Find the sum: Σfᵢ = 3+10+11+8+3 = 35 and Σfᵢxᵢ = 150+600+770+640+270 = 2430

  5. Step 5: Mean = Σfᵢxᵢ / Σfᵢ = 2430/35 = 69.43%

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