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The mean of 100 observation is 50. If on...

The mean of `100` observation is `50.` If one of the observation which was `50` is replaced by `150,` the resulting mean will be

A

`50.5`

B

51

C

`51.5`

D

`52`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, mean of `100` observation is `50.`
Here, `n=100` and `barx=100`
Then, mean `=(underset(i=1)overset(n)Sigmax_(i))/(n)`
`therefore 1/100 xx underset(i=1)overset(100)Sigmax_(i)=50 rArr underset(i=1)overset(100)x_(i)=5000`……………(i)
Now, the observation 50 is replaced by 150, then Eq. (i) becomes,
`underset(i=1)overset(100)Sigmax_(i)=5000-50+150=5100`
`therefore` Resulting mean `=(underset(i=1)overset(100)Sigmax_(i))/100 = 5100/100=51`
Hence, the resulting mean is `51.`
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