Question

Class X students appeared for a test and Marks obtained are formulated in a table
as follows (out of 80)
From the following data of the marks obtained by students of class X
Marks
0-10 10-20 20-30 30-40 40-50 50-60
No. of Students 8 12 20 30 10 10

find the upper limit of median class is......​​

Answer 1

Given :

Marks                  : 0-10    10-20    20-30    30-40    40-50    50-60

No. of Students :   8          12           20         30           10          10

To find :

The upper limit of median class.

Solution :

Marks                             : 0-10    10-20    20-30    30-40    40-50    50-60

No. of Students            :   8          12           20         30           10          10

Cumulative frequency :   8          20          40         70           80         90

Total number of students (n) = 90

n/2 = 90/2 = 45

As 45 < 70

So, 30 - 40 is the median class.

Lower limit of the median class (l) = 30

Upper limit of median class (u) = 40

Size of the class interval (h) = 40 - 30 = 10

Frequency of the median class (f) = 30

Cumulative frequency of class preceding the median class (F) = 40

$Median = l + \frac{\frac{n}{2}-F }{f} *h\\\\Median = 30 + \frac{\frac{90}{2}-40 }{30}*10\\\\Median = 30 +\frac{45 - 40}{30} *10\\\\Median = 30 + \frac{5}{30} *10$

Median = 30 + 1.67

Median = 31.67

Answer 2

Answer:

Marks                  : 0-10    10-20    20-30    30-40    40-50    50-60  

No. of Students :   8          12           20         30           10          10

Cumulative frequency :   8          20          40         70           80         90

Total number of students (n) = 90

n/2 = 90/2 = 45

As 45 < 70

So, 30 - 40 is the median class.

Lower limit of the median class (l) = 30

*Upper limit of median class (u) = 40*

_just in case you need the median_

Size of the class interval (h) = 40 - 30 = 10

Frequency of the median class (f) = 30

Cumulative frequency of class preceding the median class (F) = 40

Median = 30 + 1.67

*Median = 31.67*