If the median of the following frequency distribution is 28.5 find the missing frequencies:
Class interval:
0−10
10−20
20−30
30−40
40−50
50−60
Total
Frequency:
5
f1
20
15
f2
5
60
Answers
SOLUTION :
CUMULATIVE FREQUENCY TABLE is in the attachment.
Given : Median = 28.5, which belongs to the class 20 - 30 . So the Median class is 20 - 30
Given : n(Σfi) = 60
Here, n = 60
n/2 = 30
Here, l = 20, f = 20, cf = (5 + f1) , h = 10
MEDIAN = l + [(n/2 - cf )/f ] ×h
28.5 = 20 +( 30−(5 + f1)/20] ×10
28.5 -20 = [ (30 - 5 - f1 )/20 ] ×10
8.5 = (25 - f1)/2
8.5 × 2 = 25 - f1
17 = 25 – f1
f1 = 25 – 17
f1 = 8
Σfi = 45 + f1 + f2
60 = 45 + f1 + f2 [Σfi = 60] [f1 = 8]
60 - 45 = 8 + f2
15 - 8 = f2
f2 = 7
Hence, the missing frequencies be f1 = 8 and f2 = 7 .
MEDIAN for the GROUPED data :
For this we find the Cumulative frequency(cf) of all the classes and n/2 , where n = number of observations.
Now, find the class whose Cumulative frequency is greater than and nearest to n/2 and this class is called median class,then use the following formula calculating the median.
MEDIAN = l + [(n/2 - cf )/f ] ×h
Where,
l = lower limit of the median class
n = number of observations
cf = cumulative frequency of class interval preceding the median class
f = frequency of median class
h = class size
HOPE THIS ANSWER WILL HELP YOU.
