Question

If the median of the data : 24, 25 ,26, x+2, x+3, 30, 31, 34 is 27.5 . Then find the value of x.

Answer 1

n = 8 (even)

Median = [( n/2)th term + (n/2 + 1)th term] / 2

27.5 = [ (8/2)th term + (8/2 + 1)th term] /2

27.5 = (4th term + 5th term )/ 2

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

=> 2x + 5 = 55

=> 2x = 50

=> x = 25

Answer 2

Hey!!

Good Evening

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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 =

$\frac{( { \frac{n}{2}) }^{th \: ob.} + {( \frac{n}{2} + 1)}^{th \: ob.} }{2}$


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 ✌️

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