Question

Following distribution gives the marks scored by a class of 20 students. If 10 students scored below
14.4 and remaining 10 scored above 14.4, find values of x and y.
Marks
I 06 I 6-12 I 12-18 I 18-24 I 2430
No. of Students 4
x
5
y
1
..​

Answer 1

x = 4  and y = 6

Step-by-step explanation:

Marks     0-6 ; 6-12 ; 12-18 ; 18-24 ; 24-30

Student    4   ; x       ; 5        ; y        ; 1

Total number of student = 20

So we get x + y = 10 -----(1)

Median = 14.4

Median class is 12-18.

Median = L + (n/2-C) / f  * w

14.4 = 12 + [20/2 - (4+x)]/ 5 * 6

14.4 * 5 = 60 + (10 - 4 - x) * 6

72 = 60 + 60 - 24 - 6x

6x = 120 - 24 - 72

6x = 24

x = 24/ 6

x = 4

Substituting in (1), we get 4+ y = 10

Therefore y = 6.

Answer 2

Answer:

Step-by-step explanation:

Marks     0-6 ; 6-12 ; 12-18 ; 18-24 ; 24-30

Student    4   ; x       ; 5        ; y        ; 1

Total number of student = 20

So we get x + y = 10 -----(1)

Median = 14.4

Median class is 12-18.

Median = L + (n/2-C) / f  * w

14.4 = 12 + [20/2 - (4+x)]/ 5 * 6

14.4 * 5 = 60 + (10 - 4 - x) * 6

72 = 60 + 60 - 24 - 6x

6x = 120 - 24 - 72

6x = 24

x = 24/ 6

x = 4

Substituting in (1), we get 4+ y = 10

Therefore y = 6.