The median of the distribution given below 14.4 find the value of x and y if the total frequency is 20
Answers
Answer:
Solution :
Class Interval Frequency Cumulative Frequency
0-6 4 4
6-12 X 4+X
12-18 5 9+X
18-24 Y 9+X+Y
24-30 1 10+x+Y
---------------------------------------------------------------------------------
Total 20
∴X+Y+10=20
⇒X+Y=20-10
⇒X+Y=10 -----------
Given Median =14.4
So Median Class is 12-18
↓
12-18 5 9+X
By using formula:
Median =L+[N/2 -F] x (c/f)
where ,
L= Lower limit of median class= 12
N=20⇒N/2=20/2=10
F=Cf=Cumulative frequency of class before the median class=4+X
f=frequency of median class=5
Class interval =c=6
∴ 14.4=12+[10-[4+X)]6/5
⇒14.4-12=[10-4-X]6/5
⇒2.4=([6-X]6/5
⇒5x2.4=6[6-X]
⇒12=36-6x
⇒12-36=-6X
⇒-24= - 6X
⇒X=24/6 = 4 ----------(2)
Now, substitute the value of X in equation 1 we get the value of Y
X+Y=10
4+Y=10
Y=10-4=6
∴X=4 and Y=6