If median is 48 and cf is 229 find the 2 missing frequencies
CI Frequencies
10-20 12
20-30 30
30-40 f1
40-50 65
50-60 f2
60-70 25
70-80 18
Answers
Solution:
The given question is incorrect.
The correct question : If median is 48 and cf is 230 find the 2 missing frequencies
CI Frequencies :
10-20 12
20-30 30
30-40 f1
40-50 65
50-60 f2
60-70 25
70-80 18 .
Class interval Frequency (f) Cumulative frequency (CF)
10-20 12 12
20-30 30 42
30-40 f1 42+f1
40-50 65 107+f1
50-60 f2 107+f1+f2
60-70 25 132+f1+f2
70-80 18 150+f1+f2
We have, Median = 46 , it lies between the class interval 40-50 , so that 40-50 is the median
∴ l = 40, h = 10, f = 42+f1 and N = 230
now, we know that Median =
l+ ( 4/2-F)/(f )×h
46 = 40+((230/2-42-f1))/(65 ) ×100
3 = ((73-f1))/13
Therefore f1 = 34
now, f1 = 34 we have , N = 230
therefore 150+f1+f2 = 230 therefore
f2 = 46
hence the missing terms f1 and f2 are 34 and 46 .
If median is 48 and cf is 229 find the 2 missing frequencies
CI Frequencies
10-20 12 12
20-30 30 42
30-40 f1 42+f1
40-50 65 107+f1
50-60 f2 107+f1+f2
60-70 25 132+ f1+f2
70-80 18 150+f1+f2
cumulative frequency = 150+f1+f2 = 229
=> f1+f2 = 79
median given = 48
48 is in between 40-50
frequency of 40-50 = 65
cf for 30-40 = 42+f1
Estimated Median = L + { ( (n/2) − B)/ G}× w
L = 40 n = 229 B = 42+f1 G =65 w = 10
48 = 40 + {((229/2) - (42 +f1))/65}×10
=>8 ×65/10 = 114.5 - 42 - f1
=> 52 = 72.5 - f1
=> f1 = 72.5 - 52
=> f1 = 20.5
=> f1 = 21
f1 + f2 = 79
f2 = 79 -21 = 58