Question

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If median of data(arranged in ascending order) 5,8,11,16+x,18+x, 28, 31,40 is 18, find the value of x.​

Answer 1

observations= 5,8,11,16+x,18+x,28,31,40
total observations(n)=8(even)
median= 18
we know formula for calculating median for even no= ((n/2+1)+(n/2))/2
18= ((8/2+1)+(8/2))/2
18=((5)th+(4)th observations)/2
18=((18+x)+(16+x))/2
18=(18+x+16+x)/2
18=(34+2x)/2
18 X 2=34+2x
36=34+2x
36-34=2x
2=2x
2/2=x
which implies,,, x=1

hence the value of x=1


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Answer 2

Answer:

Number of observations = 11

Median = (n+1/2)th observation

=(11+1/2)th observation

= (12/2)th observation

= 6th observation

= x+4

x+4 = 24

x = 24-4

= 20

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