Find median of the distribution given below is 14.4, find the value of x and y if the sum of the frequency is 20
Ci 0—6,6—12,12—18,18—24,24—30
F 4 x 5 y 1
Answers
Answered by
371
Solution :-
I think there is a mistake done while typing of this question. I suppose 14.4 is the Median of the given distribution.
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
______________________________________________
20
______________________________________________
10 + x + y = 20
x + y = 20 - 10
x + y = 10
Median = 14.4
So, Median class is 12 - 18
Median = l + [(N/2 - cf)*i]/f
l = Lower limit of the Median Class = 12
Class Interval = i = 6
Cumulative Frequency (cf) of the class before the Median Class = 4 + x
N = 20
N/2 = 20/2 = 10
f = frequency of the Median Class = 5
⇒ Median = l + [(N/2 - cf)*i]/2
⇒ 14.4 = 12 + {10 - (4 + x)*6]/5
⇒ 14.4 - 12 = {(10 - 4 - x)*6}/5
⇒ 2.4 = {(6 - x)*6}/5
⇒ 2.4 = (36 - 6x)/5
⇒ 2.4*5 = 36 - 6x
⇒ 12 = 36 - 6x
⇒ - 6x = 12 - 36
- 6x = - 24
⇒ 6x = 24
x = 24/6
x = 4
Since, x + y = 10
4 + y = 10
y = 10 - 4
y = 6
So, the value of x is 4 and the value of y is 6.
Answer.
I think there is a mistake done while typing of this question. I suppose 14.4 is the Median of the given distribution.
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
______________________________________________
20
______________________________________________
10 + x + y = 20
x + y = 20 - 10
x + y = 10
Median = 14.4
So, Median class is 12 - 18
Median = l + [(N/2 - cf)*i]/f
l = Lower limit of the Median Class = 12
Class Interval = i = 6
Cumulative Frequency (cf) of the class before the Median Class = 4 + x
N = 20
N/2 = 20/2 = 10
f = frequency of the Median Class = 5
⇒ Median = l + [(N/2 - cf)*i]/2
⇒ 14.4 = 12 + {10 - (4 + x)*6]/5
⇒ 14.4 - 12 = {(10 - 4 - x)*6}/5
⇒ 2.4 = {(6 - x)*6}/5
⇒ 2.4 = (36 - 6x)/5
⇒ 2.4*5 = 36 - 6x
⇒ 12 = 36 - 6x
⇒ - 6x = 12 - 36
- 6x = - 24
⇒ 6x = 24
x = 24/6
x = 4
Since, x + y = 10
4 + y = 10
y = 10 - 4
y = 6
So, the value of x is 4 and the value of y is 6.
Answer.
prmkulk1978:
Sir, Please check the formula : its written i/2
Sorry. it is i/f but it is written correctly in the beginning of the solution.
Sorry, it should be i/f but it is written correctly in the beginning of the solution.
no problem.. sir..
Answered by
127
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 ------------(1)
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
****************************************************************************************
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 ------------(1)
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
Similar questions