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

Answer 1

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.