Question

If the median of the data: 6, 7, x − 2, x, 17, 20, written in ascending order, is 16. Then x =
(a)15
(b)16
(c)17
(d)18

Answer 1

SOLUTION :

The correct option is (c) : 17

Given : Median = 16 , observations are arrange in ascending order  : 6, 7, x − 2, x, 17, 20

Total number of observations = 6

n = 6 (even)  

If n is even then median = ½value of [ (n/2)th + (n/2 +1) th] observations.

Median = ½[(6/2)th + (6/2 + 1) th] observations

Median = ½ [3th + 4th] observations  

16 = ½ [(x - 2) + x  

16 × 2 = 2x - 2

32 = 2x - 2

2x = 32 + 2

2x = 34

x = 34/2 = 17

x = 17

Hence, the value of x is 17.

★★ Median of the data depends on the number of observations (n) .

i) If n is odd then median= value of [(n+1)/2]th observation

ii) If n is even then median= ½value of [ (n/2)th + (n/2 +1) th] observations.

HOPE THIS ANSWER WILL HELP YOU…….

Answer 2

median=16
total observation=6 let n=6
so,median=n/2+n/2+1/2
=6/2+6/2+1/2
=3+4/2
=since,third observation=x-2 & fourth observation=x
so,x-2+x/2=16
2x-2/2=16
by cross multiplication:
2x-2=32
2x=34
×=17
so,third observation=x-2=17-2=15
fourth observation=x=17
mean=6+7+15+17+17+20/6
=82/6
=13.67(approx)