Question

The mean of marks scored by 100 students was found to be 40. Later on it was discovered that a score of 53 was misread as 83. Find the correct mean.How do you so,ve this?

Answer 1

mean score = 40

mean=sum of observation /no of observations
  
sum of observations = mean x no of observations
 
that is 40 x 100
     
           = 4000

after replacement, sum of new observation=4000-83+53
                                                                    =3970

mean of new observation = 3970/100
                                         =39.7

          

Answer 2

Answer:

39.70 is the correct mean .

Step-by-step explanation:

Explanation:

Given , means of marks scored by 100 student = 40

But later on it was discovered that a scored of 53 was misread as 83 .

Step 1:

Mean = $\frac{ sum of observation }{ Total \ number of observation }$

Therefore , Mean of student = $\frac{sum of the \ marks\ of \ the\ student }{Total number\ of \ student }$

⇒ 40 = $\frac{sum of the\ marks \ of \ the\ students}{100}$

⇒ Sum of the marks of the students = 40  × 100 = 4000

Now ,according to the question a score of 53 was misread as 83 .

∴ the difference in score by mistake = 83- 53 = 30

Step 2:

So , the sum of the marks of the students = 4000 - 30 = 3970.

Actual mean = $\frac{sum of the\ marks \ of the \ students}{Total \ numbers \ of\ students }$

⇒mean = $\frac{3970}{100}$ =  39.7 0

Final answer:

Hence , the correct mean is 39.70 .

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