Question

The mean of a hundred observations was found to be 40. Later on,it was discovered that a score of 27 was misread as 57.Find the correct mean.(IT'S ANSWER IS 39.7 I NEED FULL EXPLANATION)​

Answer 1

Answer:

Mean score = 40

mean=sum of observation /no of observations

sum of observations = mean × no of observations

40 x 100→40x100

→4000

after replacement, sum of new observation=4000-57+27

3916/100

=39.16

Answer 2

Answer:

The correct mean of marks scored by  $100$ students are $39.7$

Step-by-step explanation:

We are given that

Total observations $=100$

Mean score $=40$

After discovering,

Mean score$=27$

To Find:

We need to find the correct mean.

Formula used:

$mean=\dfrac{sum\, of \,observation} {no \,of \,observations}$

Solution:

Now, we know the formula of mean is

$mean=\dfrac{sum\, of \,observation} {no \,of \,observations}$

or

$sum \,of \,observations = mean * no\, of\, observations$

Now we substitute all the given value, we get

$sum\,of\,observations=40\times100\\sum\,of\,observations=4000$

After replacement, that is $27$ was misread as $57$

Thus, the sum of new observations is:

$sum\, of\, new\, observation=4000-57+27\\sum\, of\, new\, observation=3916$

Therefore, the mean of observations:

$mean\, of\, new\, observation = \dfrac{3916}{100}\\ mean\, of\, new\, observation =39.16$

Hence, the correct mean of students are $\bold{39.16}$

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