the median of the following data is 20.75 find the missing frequency x and y a if the total frequency is hundred
Answers
Given :
Median = 20.75
Total frequency = 100
Class Interval Frequency
0 - 5 7
5 - 10 10
10 - 15 x
15 - 20 13
20 - 25 y
25 - 30 10
30 - 35 14
35 - 40 9
To find :
The missing frequency x and y.
Solution :
CI f cf
0 - 5 7 7
5 - 10 10 17
10 - 15 x 17 + x
15 - 20 13 30 + x
20 - 25 y 30 + x + y
25 - 30 10 40 + x + y
30 - 35 14 54 + x + y
35 - 40 9 63 + x + y
63 + x + y = 100
x + y = 100 - 63
x + y = 37 ......... (1)
Where,
L is the lower class boundary of the group containing the median
n is the total number of values
cf is the cumulative frequency of the groups before the median group
f is the frequency of the median group
w is the group width
20.75 - 20 = (50 - 30 - x) / y × 5
0.75y = (20 - x) × 5
3/4 × y= 100 - 5x
3y = 400 - 20x
3y + 20x = 400 .............(2)
Solve equation (1) and (2)
x + y = 37
20x + 3y = 400
Multiply equation (1) by 3 and subtract both the equations
3x + 3y = 111
20x + 3y = 400
(-) (-) (-)
-17x = -289
17x = 289
x = 17
Putting value of x in equation (1)
x + y = 37
17 + y = 37
y = 37 - 17
y = 20
Therefore, the missing frequencies x and y are 17 and 20 respectively.
Answer:
how 3/4 came and 3y has came