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If the median of $10, 12, x, 6, 18$ is $10$ , then which of the following is correct.

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x < 6; x \leq 10; 6 < x \leq 10

x > 6 x < 18

Both 1 & 2

None of the above

answer is A.

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Detailed Solution

The given data is

10, 12, x, 6, 18

. It is mentioned that its median is

10

.
We know that the median is defined as the middle number in a sorted set of data.
We can sort the data in ascending order [except

x

] as follows:

6, 10, 12, 18

We know that,

Median = (\frac{n + 1}{2})^{th} term

when

n

is odd.

Median = \frac{(\frac{n}{2})^{th} Observation + (\frac{n}{2} + 1)^{th} Observation}{2}

when

n

is even.
In the given data,

n = 5

which is odd.
Therefore,

Median = (\frac{n + 1}{2})^{th} term

\Rightarrow 10 = (\frac{5 + 1}{2})^{th} term

\Rightarrow 10 = 3^{rd} term

For 10 to be the

3^{rd}

term,

x

must either be the

1^{st}

2^{nd}

term.
Therefore, the possibilities are as follows:

\Rightarrow x \leq 10

\Rightarrow x < 6

\Rightarrow 6 < x \leq 10

Thus,

x < 6; x \leq 10; 6 < x \leq 10

.
Hence, the correct option is 1.

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