If the median of 33, 28, 20, 25, 34, x is 29, find the maximum possible value of x.
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 4thposition 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`
Here it is given that the median is 29. So, we have
` (28+x)/2 =29`
⇒28 +x =58
⇒ x = 58-28
⇒ x = 30
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