Question

Calculate the median from the following data:
Marks below:
10
20
30
40
50
60
70
80
No.of students:
15
35
60
84
96
127
198
250

Answer 1

SOLUTION :  

CUMULATIVE FREQUENCY TABLE is in the attachment.  

From the table,  Here, n = 250

n/2 = 125

Since, the Cumulative frequency just greater than 125 is 127 and the corresponding class is 50 - 60 .  Therefore 50 - 60  is the median class.

Here, l = 50 , f = 31 , c.f = 96 ,  h = 10

MEDIAN = l + [(n/2 - cf )/f ] ×h

= 50 + [125 - 96)/31] × 10

= 50 + (29/31)×10

= 50 + ( 290/31)

= 50 + 9.35

= 59.35

Hence, the Median is 59.35.

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

Concept Introduction: Median is the central observation.

Given:

We have been Given:

Class Size:

$10 - 20 \\ 20 - 30 \\ 30 - 40 \\ 40 - 50 \\ 50 - 60 \\ 60 - 70 \\ 70 - 80$

No. of Students(Frequency):

$15 \\ 20 \\ 25 \\ 24 \\ 12 \\ 37 \\ 71 \\ 52$

Therefore, Cumulative Frequency,

$15 \\ 35 \\ 60 \\ 84 \\ 96 \\ 127 \\ 198 \\ 250$

Therefore,

$n = 250$

So,

$\frac{n}{2} = 125$

Therefore,

$c.f. = 127$

and Corresponding Median Class is,

$50 - 60$

therefore,

$l = 50$

$f = 31$

$c.f. \: of \: class \: interval \: preceding \: median \: class = 96$

$h = 10$

therefore, according to Median Formula,

$m = l +(( \frac{n}{2} - c.f.) \div f)) \times h$

therefore,

$50 + ((125 - 96) \div 31) \times 10 = 50 + \frac{29 \times 10}{31} = 50 + \frac{290}{31} = 50 + 9.35 = 59.35$

Hence, the Median of the following information given is,

$59.35$

Final Answer: The Median of the following information is

$59.35$

#SPJ2