Question

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.




Weight (in kg)



40 − 45



45 − 50



50 − 55



55 − 60



60 − 65



65 − 70



70 − 75





Number of students



2



3



8



6



6



3



2

Answer 1

See the attach file for ur ans

Answer 2

Answer:

The median of the data is 56.66.

Step-by-step explanation:

Given : The distribution below gives the weights of 30 students of a class.

To find : The median weight of the students?

Solution :

Weight (in kg)      Number of students            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

The total number of terms =7

Maximum cf is N= 30

$\frac{N}{2}=\frac{30}{2}=15$

nearest to 15 is cf=13

So, The median row is 55-60

L is the lower range = 55 with frequency f=6

h is the interval size = 60-55=5

The formula of median is given by,

$M=L+[\frac{N}{2}-cf]\times \frac{h}{f}$

Substitute the values in the formula,

$M=55+[\frac{30}{2}-13]\times \frac{5}{6}$

$M=55+[15-13]\times \frac{5}{6}$

$M=55+2\times \frac{5}{6}$

$M=55+1.66$

$M=56.66$

Therefore, The median of the data is 56.66.