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UPSC CDS I 2025 Mathematics Paper

Question Numbers: 93-95

Circulation figures (in thousands) of different newspapers (A, B, C, D, E) for five years are given below:

Year	A	B	C	D	E
2019	20	10	15	8	20
2020	12	12	18	12	12
2021	24	14	17	14	15
2022	26	10	16	15	9
2023	22	16	14	16	11

Question : 93 of 100

Marks: +1, -0

In which of the given years was the circulation of the newspaper D close to its average circulation over all the years?

2020 and 2021
2022 and 2023
2022 only
2020 only

Validate

Solution:

Concept:

The average circulation is the sum of all yearly circulations divided by the number of years. The years closest to the average have the smallest absolute difference from it.

Explanation:

The circulations of newspaper D for 2019–2023 (in thousands) are: 8, 12, 14, 15, and 16.

Sum =

8 + 12 + 14 + 15 + 16 = 65

thousands.

Average =

65 \div 5 = 13

thousands.

Find absolute differences from 13:

2019: |8 - 13| = 5

2020: |12 - 13| = 1

2021: |14 - 13| = 1

2022: |15 - 13| = 2

2023: |16 - 13| = 3

The smallest difference (1 thousand) occurs in 2020 and 2021.

Answer:

A. 2020 and 2021

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