Question

If the median of the data: 24, 25, 26, x + 2, x + 3, 30, 31, 34 is 27.5, then x =
(a)27
(b)25
(c)28
(d)30

Answer 1

SOLUTION :

The correct option is (b) : 25

Given : Median = 27.5 , observations are : 24, 25, 26, x + 2, x + 3, 30, 31, 34

Total number of observations = 8  

n = 8 (even)  

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

Median = ½[(8/2)th + (8/2 + 1) th] observations

Median = ½ [4th + 5th] observations  

27.5  = ½ [(x + 2) + (x + 3)  

27.5 × 2 = 2x + 5

55 = 2x + 5

2x = 55 - 5

2x = 50

x = 50/2 = 25  

x = 25  

Hence, the value of x is 25 .

★★ 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

Hey!!

Good afternoon

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First of all this is a raw data

Thus here n = 8(even)

Here we have a formula for even number of observations

The formula is

M =




So

here (n/2)th observation is 4th observation

and (n/2 + 1)th observation is 5th observation

Thus

M = (x + 2 + x + 3)/2

Thus

=> 27.5 = (2x + 5)/2

=> 2x + 5 = 55

=> 2x = 50

=> x = 25 <<<<<<<< Answer

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Hope this helps ✌️