Answer in Brief

If the median of 33, 28, 20, 25, 34, x is 29, find the maximum possible value of *x*.

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#### Solution

The given data is 33,28,20,25,34,x. The total number of values is n = 6 , is an even number. Hence the median depends on the `(6/2)= 3^(nd)` observation and `(6/2+1) = 4^(th)`observation.

Since we have to find the maximum possible value of *x.*So we must put it in the 4^{th}position when ordering in ascending order.

Arranging the data in ascending order, we have 20,25,28,x,33,34

Hence, the median is

`((n/2)^(th) observation + (n/2+1)^(th) observation )/2`

`((6/2)^(th) observation + (6/2+1)^(th) observation )/2`

`=(3^(nd) observation + 6^(th) observation )/2`

`= (28+x)/2`

Here it is given that the median is 29. So, we have

` (28+x)/2 =29`

⇒28 +x =58

⇒ x = 58-28

⇒ x = 30

Concept: Measures of Central Tendency

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