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UPSC CDS 2 2020 Math Paper

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Question : 2 of 100

Marks: +1, -0

What is the median of 2, 4, 6, …, 100?

48
49
50
51

Solution:

We have,

2, 4, 6, …… , 100

So, here n numbers in this A.P. series.

We know that

T_{n}=a+(n-1)d

\Rightarrow 100=2+(n-1)2

\Rightarrow n-1=49

\Rightarrow n=50

Since there are 50, an even number of items . Therefore median is the arithmetic mean of

\left(\frac{50}{2}\right)^{\text{th}}

and

\left(\frac{50}{2}+1\right)^{\text{th}}

observations.

So,

25^{\text{th}}

observation

=2+(25-1)2=50

\& 26^{\text{th}}

observation

=2+(26-1)2=52

Median

=\frac{50+52}{2}=51

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