3. Median Example
Median :
After arranging the observations in ascending (or descending) order, then the middle number is called median.
It is denoted by `M`
1. If `n` is odd, then
`M=` value of `((n+1)/2)^(th)` observation
2. If `n` is even, then
`M=(text{Value of } (n/2)^(th) text{ observation} + text{Value of } (n/2 + 1)^(th) text{ observation})/2`
1. Find the Median of `4,14,12,16,6,3,1,2,3`
Solution:
Median :
Observations in the ascending order are :
`1,2,3,3,4,6,12,14,16`
Here, `n=9` is odd.
`M=` value of `((n+1)/2)^(th)` observation
`=` value of `((9+1)/2)^(th)` observation
`=` value of `5^(th)` observation
`=4`
2. Find the Median of `69,66,67,69,64,63,65,68,72`
Solution:
Median :
Observations in the ascending order are :
`63,64,65,66,67,68,69,69,72`
Here, `n=9` is odd.
`M=` value of `((n+1)/2)^(th)` observation
`=` value of `((9+1)/2)^(th)` observation
`=` value of `5^(th)` observation
`=67`
3. Find the Median of `3,23,13,11,15,5,4,2`
Solution:
Median :
Observations in the ascending order are :
`2,3,4,5,11,13,15,23`
Here, `n=8` is even.
`M=(text{Value of } (n/2)^(th) text{ observation} + text{Value of } (n/2 + 1)^(th) text{ observation})/2`
`=(text{Value of } (8/2)^(th) text{ observation} + text{Value of } (8/2 + 1)^(th) text{ observation})/2`
`=(text{Value of }4^(th) text{ observation} + text{Value of }5^(th) text{ observation})/2`
`=(5 + 11)/2`
`=8`
This material is intended as a summary. Use your textbook for detail explanation.
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