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Question
The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be ______.
Options
50.5
51
51.5
52
Solution
The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be 51.
Explanation:
Given, mean of 100 observations is 50.
Here, n = 100 and `barx` = 100
Then, mean = `(sum_(i = 1)^n x_i)/n`
∴ `1/100 xx sum_(i = 1)^100 x_i = 50`
⇒ `sum_(i = 1)^100 x_i = 5000` ...(i)
Now, the observation 50 is replaced by 150, then equation (i) becomes,
`sum_(i = 1)^100 x_i = 5000 - 50 + 150 = 5100` ...(ii)
∴ Resulting mean = `(sum_(i = 1)^100 x_i)/100 = 5100/100 = 51` ...[From (ii)]
Hence, the resulting mean is 51.
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