Question

10 observations 6, 14, 15, 17, X + 1, 2x - 13, 30, 32, 34, 43, written in ascending order the medium of the data is 24 find the value of x

Answer 1

  No: of observations = 10 
As the No: of observations is even ,
 Median = [( n/2th observation) + (n/2)+1 th observation] ÷ 2
n/2 th observation = 5 th observation = x+1
(n/2)+1 th observation = 6th observation = 2 x-13
[x+1 + 2x -13] ÷ 2 = median
[x+1 + 2x -13] ÷ 2 = 24
(3x - 12) ÷ 2 = 24
3x - 12 = 24 × 2 
3x - 12 = 48
3x = 48 + 12
3x =  60
x = 60 ÷ 3 
∴ x = 20

Answer 2

No. of observation=10(even)

Median(even)=1/2{n/2 th term +(n/2+1)th term)}


24=1/2{10/2 th term+(10/2+1) th term}

24=1/2{5th term+(5+1)th term}

24=1/2(5th term+6th term)

24=1/2(x+1+2x-13)

24=1/2(3x-12)

24×2=3x-12

48=3x-12

3x=48+12

3x=60

x=60/3

x=20.