Question

In a batch of 20 students, 8 students failed in a test. The marks of 12 students
who passed were as follows. What was the Median of the marks of all the 20
students?
18, 12, 14, 16, 16, 18, 12, 10, 8, 14, 20, 13​

Answer 1

Answer:

15 is the median of this numbers

middle two numbers is 18and12

sum the middle number

and divide by 2 then the number is your answer

18+12=30

30÷2

=15

Answer 2

Given: In a batch of 20 students, 8 students failed in a test. The marks of 12 students who passed were as follows:

18, 12, 14, 16, 16, 18, 12, 10, 8, 14, 20, 13

To find: The median of the marks of all 20 students

Solution: The students who have failed the exam must have scored lower marks than the passed student with the least marks, that is, 8.

Let their marks be a,b,c,d,e,f,g and h in increasing order.

For finding the median of the number, all the numbers are arranged in ascending order. On arranging the numbers, the term which is in the middle is the median.

Arranging the given marks in ascending order:

a, b, c, d, e, f, g, h, 8, 10, 12, 12, 13, 14, 14, 16, 16, 18, 18, 20

Since the number of terms is even, there are two middle terms and the average of those middle terms is the median.

The middle terms are n/2 and (n/2) +1

Since n = 20 , middle terms are 10th term and the (10+1)= 11th term.

10th term = 10

11th term= 12

Median of marks of students

= 10th term + 11th term / 2

= 10+12/2

= 11

Therefore, the median of marks of all 20 students is 11.