Test Index

UPSC CDS 2 2023 Math Paper

Question Numbers: 47-48

Consider the following for the next items that follow:

A grouped frequency distribution is given below:

Question : 47 of 100

Marks: +1, -0

Solution:

Concept:

Use the formula for weighted mean to find the missing frequency

k

Explanation:

The average weekly wage is given as Rs. 3,520.

First, calculate the midpoint

x(i)

for each wage class and multiply by the number of workers

f(i)

Set up the average formula:

3520 = \frac{126500 + 3300k}{35 + k}

Cross-multiply:

3520(35 + k) = 126500 + 3300k

Simplify:

123200 + 3520k = 126500 + 3300k

Rearrange:

3520k - 3300k = 126500 - 123200

220k = 3300

Divide:

k = 15

Answer:

k = 15

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