# Mean of 100 observations is 45. It was later found that two observations 19 and 31 were incorrectly recorded as 91 and 13. The correct mean

As learnt in

ARITHMETIC Mean -

For the values x1, x2, ....xn of the variant x the arithmetic mean is given by

$\dpi{100} \bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}$

In case of discrete data.

-Given that, $45 = \frac{x_{1}+ x_{2}+\cdot \cdot \cdot \ x_{100}}{100}$

$\therefore x_{1}+x_{2}+\cdot \cdot \ x_{100} = 4500$

But two numbers (19+31 = 50) were incorrect

So, net sum = 4500 - 50 = 4450

Add correct numbers (91+13 = 104)

⇒ 4450 +104 = 4554

⇒ new mean = 4554/100 = 45.54

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