Question 5 of 21intermediate🔧 ApplyNumerical4 marks

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoes50 - 5253 - 5556 - 5859 - 6162 - 64
Number of boxes1511013511525

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Correct Answer

The mean number of mangoes kept in a packing box is 57.19 (or 57.1875). I chose the Direct Method because the class sizes are equal and the values of frequencies and mid-points are manageable for direct calculation.

Exercise: EXERCISE 13.1 | Q: 5 | (Page 12)
For More Understanding

Explanation

This question requires finding the mean of grouped data. The Direct Method is suitable here as the frequencies and class marks result in calculations that are easy to handle. Students need to find class marks (mid-points), multiply them with corresponding frequencies, and apply the mean formula.

Solution Steps

  1. Step 1: Find the class mark (mid-point) for each class interval using xᵢ = (Lower limit + Upper limit)/2

  2. For 50-52: x₁ = (50+52)/2 = 51

  3. For 53-55: x₂ = (53+55)/2 = 54

  4. For 56-58: x₃ = (56+58)/2 = 57

  5. For 59-61: x₄ = (59+61)/2 = 60

  6. For 62-64: x₅ = (62+64)/2 = 63

  7. Step 2: Calculate fᵢxᵢ for each class:

  8. 15×5115 \times 51 = 765

  9. 110×54110 \times 54 = 5940

  10. 135×57135 \times 57 = 7695

  11. 115×60115 \times 60 = 6900

  12. 25×6325 \times 63 = 1575

  13. Step 3: Find the totals:

  14. Σfᵢ = 15 + 110 + 135 + 115 + 25 = 400

  15. Σfᵢxᵢ = 765 + 5940 + 7695 + 6900 + 1575 = 22875

  16. Step 4: Apply the Direct Method formula:

  17. Mean (x̄) = Σfᵢxᵢ/Σfᵢ = 22875/400 = 57.1875

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