Question

Find the mode of the following distribution of marks obtained by the students in an examination:

Marks obtained 0-20 20-40 40-60 60-80 80-100
Number of students 15 18 21 29 17

Given the mean of the above distribution is 53, using empirical relationship estimate the value of its median.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

Here modal class is 60-80, since it has a maximum frequency which is 29.


l= 60 , f1= 29, f0= 21, f2= 17, h= 20


Mode=  l + (f1-f0/2f1-f0-f2) ×h


Mode= 60 +(29-21/2×29-21-17)× 20


Mode= 60 + (8/58-21-17)× 20


Mode= 60+ (8/37-17)×20


Mode= 60 + (8/20)×20


Mode = 60 + 8


Mode = 68


Hence, the mode marks is 68.


Empirical formula between Mean ,Median& Mode:


3 Median = Mode +2 Mean


3 Median = 68 + 2(53)


[ Mean = 53 (given)]


3 Median = 68 + 106


3 Median= 174


Median= 174/3


Median = 58


Hence, the Median is 58 .


Hope this will help you....

Answer 2

Hope this will help u...pls mark it as brainliest