In a class test the mean of Mark's scored by a class of 40 students wa

1.	In a class test the mean of Mark's scored by a class of 40 students was calculated as 18.2.Later on it was detected that the marks of one student was wrongly copied as 21 instead of 29. Find the correct mean.
Answer» Correct Mean is 18.4. Step-by-step explanation: We are given that in a class test the mean of Mark's scored by a class of 40 students was calculated as 18.2. Later on it was detected that the MARKS of ONE student was wrongly copied as 21 instead of 29. As we know that, Mean formula is given by; Mean = $\frac{\text{Total sum of all the <klux>OBSERVATIONS</klux>}}{\text{Number of observations}}$ Or $\bar X =\frac{\sum X }{\text{n}}$ where, $\sum X$ = Total sum of all observations in the data n = Number of observations So, $Incorrect \sum X$ = $\bar X \times n$ {as we are given Mean = 18.2 and n = 40} = $18.2 \times 40$ = 728 Now, we are are given that it was detected that the marks of one student was wrongly copied as 21 instead of 29; So, the correct $\sum X$ =728 - 21 + 29 = 736 And the total number of students now = 40 - 1 + 1 = 40 Hence, the correct mean = $\frac{736}{40}$ = 18.4.

In a class test the mean of Mark's scored by a class of 40 students was calculated as 18.2.Later on it was detected that the marks of one student was wrongly copied as 21 instead of 29. Find the correct mean.

Answer»

Step-by-step explanation:

We are given that in a class test the mean of Mark's scored by a class of 40 students was calculated as 18.2.

Later on it was detected that the MARKS of ONE student was wrongly copied as 21 instead of 29.

As we know that, Mean formula is given by;

Mean = $\frac{\text{Total sum of all the <klux>OBSERVATIONS</klux>}}{\text{Number of observations}}$

$\bar X =\frac{\sum X }{\text{n}}$

where, $\sum X$ = Total sum of all observations in the data

n = Number of observations

So, $Incorrect \sum X$ = $\bar X \times n$ {as we are given Mean = 18.2 and n = 40}

= $18.2 \times 40$ = 728

Now, we are are given that it was detected that the marks of one student was wrongly copied as 21 instead of 29;

So, the correct $\sum X$ =728 - 21 + 29 = 736

And the total number of students now = 40 - 1 + 1 = 40

Hence, the correct mean = $\frac{736}{40}$ = 18.4.