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Question

The frequency distribution of marks of 100 candidates in a particular examination is as follows:
MarksNumber of Candidates
More than 10100
More than 2075
More than 3060
More than 4040
What are the average marks of the candidates?

This question was previously asked in
CDS 2 2025 Maths Question Paper (14-Sep-2025)
The correct answer is
32.5

To find the average marks of the candidates, we have to convert this cumulative frequency distribution into a frequency distribution, and then determine the mean.

  1. First, create intervals and frequencies:
    • Marks > 10 implies 10-20 candidates: \(100 - 75 = 25\)
    • Marks > 20 implies 20-30 candidates: \(75 - 60 = 15\)
    • Marks > 30 implies 30-40 candidates: \(60 - 40 = 20\)
    • Marks > 40 implies 40-50 candidates: \(40 - 0 = 40\)
  2. Summarize this as a frequency table:
Marks IntervalNumber of Candidates (f)
10-2025
20-3015
30-4020
40-5040
  1. Find the midpoint (x) for each interval:
    • 10-20: \(x = \frac{10 + 20}{2} = 15\)
    • 20-30: \(x = \frac{20 + 30}{2} = 25\)
    • 30-40: \(x = \frac{30 + 40}{2} = 35\)
    • 40-50: \(x = \frac{40 + 50}{2} = 45\)
  2. Calculate the sum of the products of midpoints and frequencies: \(\sum (f \cdot x) = 25 \times 15 + 15 \times 25 + 20 \times 35 + 40 \times 45\)
    • \(= 375 + 375 + 700 + 1800\)
    • \(= 3250\)
  3. Find the sum of frequencies: \(\sum f = 25 + 15 + 20 + 40 = 100\)
  4. Calculate mean (average) using the formula: \(\text{Mean} = \frac{\sum (f \cdot x)}{\sum f} = \frac{3250}{100} = 32.5\)

Therefore, the average marks of the candidates are 32.5.

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Similar Questions

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  2. What is the mode of the distribution?
  3. Consider the following data :
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Important Questions from Elementary Statistics

  1. In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.

  2. For which set of numbers do the mean, median and mode all have the same value?

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  4. Find the mean of first 5 two-digit multiples of 4.

  5. The difference between the upper limit and the lower limit of a class is called :

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