Question

The distribution below gives the weight of 30 students in a class. Find the median weight of students:
Weight (in kg):
40−45
45−50
50−55
55−60
60−65
65−70
70−75
No. of students:
2
3
8
6
6
3

Answer 1

SOLUTION :  

CUMULATIVE FREQUENCY TABLE is in the attachment.  

Here, n = 30

n/2 = 15

Since, the Cumulative frequency just greater than 15 is 19 and the corresponding class is 55 - 60 .Therefore 55 - 60 is the median class.

Here, l = 55 , f = 6, c.f = 13,  h = 5

MEDIAN = l + [(n/2 - cf )/f ] ×h

= 55 + [(15 - 13)/6] × 5

= 55 +(2× 5)/6

= 55 + 10/6

= 55 + 5/3

= 55 + 1.667

= 56.667 ≈ 56.67

Hence, the Median weight of students  is 56.67 kg .

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.  

Answer 2

Answer : 

( The table is given in the attachment )

The cumulative frequency is little greater than ( N/2 = 30/2 = 15 ) 20 which belongs to the class interval = 55-60

Median class = 55-60

l = 55
Frequency = 6
cf of class preceding median class = 13

Class size h = 5

Using formula, 
$\sf{Median = l + \frac{ \frac{n}{2} - cf }{h} \times h}$

$\sf {= 55 + \frac{15-13}{6} \times 5}$

$\sf{ =56.66 }$ 

The median weight of students is 56.66 kg.

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