Question

The mean marks of 120 students is 20. It was later discovered that two marks were wrongly taken as 50 and 80 instead of 15 and 18. The correct mean of marks is
A) 19.19
B) 19.17
C) 19.21
D) 19.14

Answer 1

Hint: In the given question, as the total number of students are 120 and as mean is given, hence first we need to find the summation of mean then, by considering that two marks were wrongly taken as 50 and 80 instead of 15 and 18 we must find the summation of correct mean, hence by this we can find the correct mean of marks.

Formula used:\[\bar x = \dfrac{{\sum x }}{n}\]
In which,
n is the total number of students.
\[\bar x\] is mean.
\[\sum x \] is a summation of the mean.

Complete step-by-step solution:
 Let us write the given data:
Given, the total number of candidates = 120
The mean marks of the students are = 20
\[\Rightarrow \bar x = \dfrac{{\sum x }}{n}\]
\[\Rightarrow 20 = \dfrac{{\sum x }}{{120}}\]
Hence, the summation of the given means marks is
\[\Rightarrow \sum x = 2400\]
Now we need to find the correct mean of marks, hence for this we need to find the summation of correct mean i.e., by considering that two marks were wrongly taken as 50 and 80 instead of 15 and 18, hence by the given data we have:
\[\Rightarrow {\left( {\sum x } \right)_{correct}} = 2400 - 50 - 80 + 15 + 18\]
\[\Rightarrow {\left( {\sum x } \right)_{correct}} = 2270 + 33\]
\[\Rightarrow {\left( {\sum x } \right)_{correct}} = 2303\]
Hence, after simplifying the correct mean of marks is:
\[\Rightarrow {\bar x_{correct}} = \dfrac{{{{\left( {\sum x } \right)}_{correct}}}}{n}\]
\[\Rightarrow {\bar x_{correct}} = \dfrac{{2303}}{{120}}\]
On solving further, we get:
\[{\bar x_{correct}} = 19.19\]

Hence the correct answer is option ‘A’.

Note: Here the students may get confused while finding the total mean and summation of mean marks with respect to correct mean of marks, hence note down the formula according to the given data respectively. We know that it was later discovered that two marks were wrongly taken as 50 and 80 instead of 15 and 18, hence considering these marks we can find the correct mean marks of the students.