Question

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

Answer 1

Answer:

Weight ( in kg ) Frequency  Cumulative frequency  

40−45 2  2  

45−50 3  5  

50−55 8  13  

55−60 6  19  

60−65 6  25  

65−70 3  28  

70−75 2  30  

 N=30    

We have N=30 and  

2

N

​  

=15.

Median class =55−60, so l=55,f=6,cf=13 and h=60−55=5

Median=l+  

f

2

N

​  

−cf

​  

×h

⇒  Median=55+  

6

15−13

​  

×5

⇒  Median=55+1.67=56.67kg

Step-by-step explanation:

Answer 2

Answer:

Answer

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weight of no. of students

students

(Class) (frequency f) (cumulative frequency cf)

40 - 45 2 2

45 - 50 3 5

50 - 55 8 13

55 - 60 6 19

60 - 65 6 25

65 - 70 3 28

70 - 75 2 30

N = total no. of students = ∑f = 30 N/2 = 30/2 = 15

the cumulative frequency just greater than 15 is 19 and the corresponding class is 55 - 60 .

therefore 55 - 60 is the median class

l = lower limit of median class = 55

f=frequency of the median class = 6

F = cumulative frequency of the class preceding the median class = 13

h = size of the median class =5

median = l+ ( [ { (N/2) - F } /f ] * h )

= 55 + ( [ { ( 30/2 ) - 13} / 6] * 5 )

= 56.66