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UPSC CDS I 2025 Mathematics Paper

Question Numbers: 86-90

The frequency distribution of 205 observations on X is given below:

x	3	5	6	7
Frequency	f	f + 2	f − 3	f + 6

Question : 90 of 100

Marks: +1, -0

What is the mean of the frequency distribution?

Solution:

Concept:

The mean of a frequency distribution is found by dividing the sum of (each value times its frequency) by the total frequency.

Explanation:

Given values:

x = 3, 5, 6, 7

and frequencies:

50, 52, 47, 56

Compute each product:

3 \times 50 = 150

5 \times 52 = 260

6 \times 47 = 282

7 \times 56 = 392

Add these:

150 + 260 + 282 + 392 = 1084

Total frequency:

50 + 52 + 47 + 56 = 205

Mean =

1084 \div 205 \approx 5.29

Answer:

C. 5·29

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