#### 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 is: Option 1) 44 Option 2) 44.46 Option 3) 45 Option 4) 45.54

As learnt in

ARITHMETIC Mean -

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

in case of discrete data.

-

Given that,

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

Option 1)

44

This option is incorrect

Option 2)

44.46

This option is incorrect

Option 3)

45

This option is incorrect

Option 4)

45.54

This option is correct