If the median of the data 6, 7, x - 2, x, 17, 20, written in ascending order, is 16. Then x is ____.

If the median of the data

6, 7, x - 2, x, 17, 20

written in ascending order, is 16. Then

x is 17

.
If the number of elements, n is odd, median will be the

n + 1 2 t h

element in the arranged distribution.
If the number of elements, n is even, median will be the mean of

n 2 t h and n 2 + 1 h

terms in the arranged distribution.
Since the distribution contains 6 elements, the median will be the mean of

3^{rd}

and

4^{th}

terms.
Here the

3^{rd}

term is

x - 2

and the

4^{th}

term is x.
⇒

Median = \frac{x - 2 + x}{2}

⇒

Median = \frac{2 x - 2}{2}

⇒

Median = \frac{2 (x - 1)}{2}

⇒

Median = x - 1

⇒

16 = x - 1

⇒

x = 17 .

Hence, the required answer is 17.

If the median of the data $6, 7, x - 2, x, 17, 20$ , written in ascending order, is 16. Then $x$ is ____.