Question

if the observation of 6,7, x - 2, x, 17,20 written in ascending order and the median is 16. find the value of x and hence find the mean of the given data

Answer 1

There are 56 observations.. And thus the median of positions 3rd and 4th wl b taken.. So x-2+x/2 = 16 2x-2/2=16 2(x-1)/2=16 x-1=16 x=17 So the other no is 15... So then the mean is 6+7+15+17+17+20/6 = 82/6 =13.6

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)