Question

Kavita obtained 16, 14, 18, and 20 marks ( out of 25 ) in maths in weekly tests in the month of Jan 2000; then the mean marks of Kavita is
(a) 16
(b) 16.5
(c) 17
(d) 14.5

Answer 1

Hint: To solve this question, firstly we will see how we find the mean marks or average marks of a student. Then, using the mean formula, we will find the mean marks of Kavita by first adding all the marks obtained by Kavita and dividing them by the number of tests she has given in the month of Jan 2000.

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 given that Kavita has given a total of four tests in the month of Jan 2000, and marks she obtained in those four tests are 16, 14, 18, and 20 respectively out of 25.
Now, the summation of all marks she obtained in four test equals 16 + 14 + 18 + 20
On simplifying, we get
Sum of all marks = 68
Now, as we discussed above the mean,
So mean marks of Kavita is
$\bar{x}=\dfrac{68}{4}$
On simplifying, we get
$\bar{x}=17$
So, the mean mark of Kavita is 17. Hence, the option ( c ) is correct.

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, there is no relation with the total number of marks the test was carrying as it is useful in only finding the percentage of students not in the mean. So, in this question, there is no need for 25 marks in the calculation. Try not to make any calculation mistakes.