Question

The average marks of 50 students in mathematics are 38. Later it is found that three marks 42, 40 and 25 were wrongly entered as 35, 30 and 28. Find the averages after mistakes were rectified?

Answer 1

$\Longrightarrow{\boxed{\bold{Answer: 38.28}}}$

$\textbf{\underline{Step-by-step explanation :- }}$

$\textbf{\underline{Since we know that,}}$

$\textbf{\large{Mean = Average}}$

Mean = ∑ / n

$\textsf{\underline{Here, Mean = 38}}$
$\textsf{\underline{and, n = 50}}$

38 = ∑ / 50

38 × 50 = 1900 = ∑

Correct ∑ = Incorrect ∑ - Incorrect value + correct value

Correct value of ∑

$\bold{\tiny{= 1900 - ( 35 + 30 + 28 ) + ( 42 + 40 + 25 )}}$

Correct ∑ $\bold{= 1900 - 93 + 107}$

Correct ∑ = $\bold{\large{1914}}$

Mean = 1914 / 50

$\bold{\underline{\huge{Mean = 38.28}}}$

Answer 2

Hello!

In this question mean and average are same.

Students:- 50

Mean:- 38

                                       N - 50

                                       M - 38

                -----------------------------------------------------------------------

We know the formula of mean

Mean = ∑/N

N = 50

Mean = 38

============================

Therefore, Mean*N

                   => 50*38

                   => 1900

                           -----------------------------------------------------------------

Now, we know that

                                         Correct value of ∑

                                      => 1900 - (42+40+25) + (35+30+25)

            (42+40+25) = 103

            (35+30+25) = 93

------------------------------------------------------------------------------------------

Therefore,

Correct ∑ = Mean*n+ 103 + 93

Correct ∑ = 1900 - 103 + 93

Correct ∑ = 1914

               

---------------------------------------------------------

Mean = ∑/N

                               Therefore, No of students = 50

                                                   Correct ∑ = 1914

------------------------

Mean = 1914 / 50

=> 38.28

                          38.28