Question

Calculate the median from the following data:
Rent (in Rs.):
15−25
25−35
35−45
45−55
55−65
65−75
75−85
85−95
No. of Houses:
8
10
15
25
40
20
15
7

Answer 1

SOLUTION :  

CUMULATIVE FREQUENCY TABLE is in the attachment.  

From the table,  Here, n = 140  

n/2 = 70

Since, the Cumulative frequency just greater than 70 is 98 and the corresponding class is 55 - 65 .  Therefore 55 - 65  is the median class.

Here, l = 55 , f = 40 , c.f =58 ,  h = 10

MEDIAN = l + [(n/2 - cf )/f ] ×h

= 55 + [70 - 58)/40] × 10

= 55 + (12/40)×10

= 55 + 120/40

= 55 + 3

= 58

Hence, the Median is 58.

MEDIAN: Median is defined as the middle most or the Central observation , when the observations are arranged either in ascending or descending order of their magnitudes.

★★Median is that value of the given observation which divides it into exactly two parts.i.e 50% of the observations lie below the median and the remaining are above the median.

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

★★ CUMULATIVE FREQUENCY:

Cumulative frequency is defined as a consecutive sum of frequencies.

**The Cumulative frequency of first observation is the same as its frequency since there is no frequency before it.

HOPE THIS ANSWER WILL HELP YOU.