Question

The mean of marks scord by 100 students
was found to be 40. later Pon it was
discoved that a score 53 was missead
as 83. Find the correct mean.
​

Answer 1

Answer:

= 3970/100  =39.7

Step-by-step explanation:

mean score is = 40

mean = sum of observation /no of observations

sum of observations = mean multiplied by the number of observations

 

That will be 40 x 100

= 4000

Now after the replacement, sum of new observation

= 4000 - 83 + 53                    

=3970

mean of new observation

= 3970/100  

=39.7

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The correct mean of the marks is 39.7

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Number of Students = 100

Mean of the marks (wrong) = 40

53 taken as 83 due to a mistake

To Find :

The Actual mean

Solution :

First, find the sum of the marks. Consider the sum as x

★ Mean = $\boxed{\sf{\frac{Sum \: of \: Observations}{No. \: of \: Observations}}}$

• Mean = 40
• Sum of Observations = x
• Number of Observations = 100

$\sf{\longrightarrow{40 = \dfrac{x}{100}}}$

$\sf{\longrightarrow{x=100 \times 40}}$

$\sf{\longrightarrow} \:x = 4000$

Sum of the Marks is 4000

$\rule{300}{1.5}$

Subtract 83 from 4000 as it was miscalculated.

$\sf{\longrightarrow} \: 4000 - 83$

$\sf{\longrightarrow} \: 3917$

$\rule{300}{1.5}$

Add 53 to 3917 to get correct sum of Marks

$\sf{\longrightarrow} \: 3917 + 53$

$\sf{\longrightarrow} \: 3970$

$\rule{300}{1.5}$

As we got the correct sum, we can now find the mean.

• Sum of Observations = 3970
• Number of Observations = 100

$\sf{\longrightarrow} \: \dfrac{3970}{100}$

$\sf{\longrightarrow} \: 39.7$

$\therefore$ The correct mean of the marks is 39.7