Question

Following observations are arranged in ascending
onder as follows 2, 3, 5, 9, x+1, x+3, 14, 16, 19, 20.
If the median of the data is 11
. Find the value of x​

Answer 1

Step-by-step explanation:

The 10 observations are arranged in ascending order as follows:

2,3,5,9,x+1,x+3,14,16,19,20

Since, the median of the data is 11.

As, the number of observations=10, which is an even number.

Median=11

⇒

2

1

[(

2

10

)thobservation+(

2

10

+1)thobservation]=11

⇒

2

1

×[5thobservation+6thobservation]=11

⇒

2

1

×[x+1+x+3]=11

⇒2x+4=2×11

⇒x=

2

18

=9×11

So, the value of x is 9.

Answer 2

Answer:

For even no. of observations:-

$median = \frac{1}{2} ( \frac{n}{2}th + ( \frac{n }{2} + 1)th \: observation)$

Median = 1/2 (x +1 + x +3)

11 = 1/2(2x +4)

22 = 2x +4

18 = 2x

x =9