Question

The following table shows the marks scored by Anju, Neelesh, and Lekhya in four-unit tests of English.

(i) Find the average marks obtained by Lekhya.
( ii ) Find the average marks secured by Anju. Will you divide the total marks by 3 or 4? Why?
( iii ) Neelesh has given all four tests. Find the average marks secured by him. Will you divide the total marks by 3 or 4? Why?
( iv ) Who performs best in English?

Answer 1

Hint: To solve this question, firstly we will find out the average of Lekhya’s marks by using the Mean formula. After that, we will find the average marks of Anju by dividing the summation of the score by 3, and the average of Neelesh by dividing the summation of the score of neelesh by 4 as he appeared in all four tests. And after that, we will compare the average marks of all three students to find out the best performer in the subject of English.

Complete step-by-step solution:
Now, before we solve this question, firstly we see what does Average or mean of data means.
Let, we have collection of data of n – terms, ${{x}_{1}},{{x}_{2}},{{x}_{3}},......,{{x}_{n}}$ , then average of these n items is denoted by $\bar{x}$ and is given by $\bar{x}=\dfrac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+......+{{x}_{n}}}{n}$.
Now, in question, it is asked to find the answer to various types of sub-questions.
(i) now, marks obtained by Lekhya in four-unit tests are 20, 24, 24, 24.
So, summation of four marks is equals to 20 + 24 + 24 + 24 = 92
Then, the mean marks of Lekhya is $\bar{x}=\dfrac{92}{4}$
On, simplifying, we get
$\bar{x}=23$
(ii) Now, as anju has not given the Unit test – 1, so her average will be taken by adding the marks of three unit tests and dividing by 3 only.
So, summation of four marks is equals to 19+ 23+ 21 = 63
Then, the marks of Anju is $\bar{x}=\dfrac{63}{3}$
On, simplifying, we get
$\bar{x}=21$
(iii) Now, as neelesh appeared for all four unit tests, it does not matter how much he gets marks in any of the tests, the average will be found by dividing summation of marks by 4.
So, summation of marks of Neelesh is 0 + 20 + 22 + 24 = 68
Then, the mean marks of Neelesh is $\bar{x}=\dfrac{68}{4}$
On, simplifying, we get
$\bar{x}=16.5$
(iv) Now, the best performer in English will be one, who has the highest average in English from others. So, on comparing the average marks of Lekhya, Anju, and Neelesh, we can clearly see that lekhya has the highest average marks which are 23.
So, Lekhya performs best in English.

Note: Always remember that, if we have data of n – terms, ${{x}_{1}},{{x}_{2}},{{x}_{3}},......,{{x}_{n}}$ , then average of these n items is denoted by $\bar{x}$ and is given by $\bar{x}=\dfrac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+......+{{x}_{n}}}{n}$. Also, we find the average of students by those number of subjects in which a student has appeared, but we do not include those subjects/tests in which students have not appeared. Try not to make any calculation mistakes.