Test Index

UPSC CDS 2 2019 Math Paper

Question Numbers: 1-2

Directions: Read the following frequency distribution for two series of observations and answer the two items that follow:

Question : 1 of 100

Marks: +1, -0

What is the mean of frequency distribution of Series-I?

Solution:

Concept:

Mean of a frequency distribution is the sum of (midpoint × frequency) divided by the total frequency.

Explanation:

First, find the missing frequencies for classes 40-50 and 50-60.

Let

X

be frequency for 40-50 and

Y

for 50-60.

From the given totals:

X + Y = 100 - (20+15+10) = 55

... (1)

Also,

2X + Y = 100 - (4+8+4) = 84

... (2)

Subtract (1) from (2):

(2X+Y) - (X+Y) = 84-55 \Rightarrow X = 29

Then

Y = 55 - 29 = 26

Now calculate the mean using the table:

Mean

= \frac{\sum x_i f_i}{\sum f_i} = \frac{3760}{100} = 37.6

Answer:

37.6 (Option C).

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