Question

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.
Age in years:
0−10
10−20
20−30
30−40
40−50
No. of persons:
5
25
?
18
7

Answer 1

SOLUTION :  

CUMULATIVE FREQUENCY TABLE is in the attachment.  

Given , Median = 24 which belongs to the class 20 - 30 , so the median class is 20 - 30.

Let the missing frequency be x.

From the table,  Here, n = 55 + x

n/2 = (55+x)/2

Here, l = 20 , f = x , c.f = 30 ,  h = 10

MEDIAN = l + [(n/2 - cf )/f ] ×h

24 = 20 + [((55+x)/2 - 30)/x] × 10

24 -  20 =   [((55+x)/2 - 30)/x] × 10

4x = [((55 + x)/2 - 30)] × 10

4x = [(55+ x) - 30× 2)/2 ] ×10

4x = [(55 + x - 60)/2 ] ×10

4x = [-5 + x ]/2 × 10

4x × 2  = -50 + 10x  

8x - 10x = -50

-2x = -50

x = 50/2 = 25

x = 25  

Hence, the missing frequency is 25.  

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.  

Answer 2

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