Question

Kindly solve this in 15 minutes, and kindly ignore it if i did not get answer on time.

Calculate mean, median and mode of the following   

class Interval:              0-9       10-19   20-29   30-39   40-49   50-59   60-69 70-79

No. of students:           9        13        27        57        64        46        31        9

Answer 1

Sol.

Class interval	no.of students (f​​​​​​i​​​)	class mark (x​​​​​i)	f​​i​​​ x​​​​​​i	cumulative frequency
-0.5-9.5	9	4.5	40.5	9
9.5-19.5	13	14.5	188.5	22
19.5-29.5	27	24.5	661.5	49
29.5-39.5	57	34.5	1966.5	106
39.5-49.5	64	44.5	2848	170
49.5-59.5	46	54.5	2507	216
59.5-69.5	31	64.5	1999.5	247
69.5-79.5	9	74.5	670.5	256

calculation of mean:-

As e know that the mean is calculated by using direct method as

Calculation of median:-

As we know that

Where

l= lower limit of the median class

n=number of observations or total frequency

cf= cumulative frequency of class preceding the median class

f=frequency of median class

h=class size

Now

n/2=256/2=128

So 39.5-49.5 is the class whose cumulative frequency 170 is greater than (or nearest to ) n/2 i.e.128

Therefore 39.5-49.5 is the median class.

Here

l=39.5, cf=106, f=64, h=10

So

calculation of mode:-

As we know that the mode of a continuous data is calculated by the formula

Where l= lower limit of modal class

f_{​​​​​​1}​​​=frequency of modal class

f_{​​​​​​0}​​​​​=Frequency of class preceding the modal class

f_{​​​​​​2}​​​=Frequency of class succeeding the modal class

h=size of the class interval

Here maximum class frequency is 64 and class corresponding to this frequency is 39.5-49.5

So modal class is 39.5-49.5

Now

l= 39.5 , f_{​​​​​​1}​​​= 64, f_{​​​​0}​=57 , f_​​​2=46, h=10

So