Question

Q5.The mean of40 numbers was found to be38.Lateron,it wad detected that a number 56 wad misread

as 36. Find the correct mean of the given numbers.​

Answer 1

Topic :-

Arithmetic Mean

Given :-

The mean of 40 numbers was found to be 38. Later on, it was detected that a number 56 was misread as 36.

To Find :-

Correct mean of given numbers.

Formula to be Used :-

$\underline {\boxed{\sf{Mean=\dfrac{Sum\:of\:all\:terms}{Number\:of\:terms}}}}$

Solution :-

It is given that mean of 40 numbers was found to be 38.

Let sum of all terms be 'x'.

Apply formula,

$\sf{38=\dfrac{x}{40}}$

$\sf{x=38 \times 40}$

$\sf {x = 1520}$

It was detected that a number 56 was misread as 36.

It means correct sum of all terms is

56 - 36 = 20 more than obtained sum of all terms.

So,

Correct Sum of terms = x + 20

Correct Sum of terms = 1520 + 20

Correct Sum of terms = 1540

Total number of terms = 40

Now, apply the formula,

$\sf{Correct\:Mean=\dfrac{1540}{40}}$

$\sf {Correct\:Mean=38.50}$

Answer :-

So, correct mean of the given numbers is 38.50.