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Question

Marks scored by 100 students in a 25 marks unit test of Mathematics is given below Their median is

  1. 12    
  2. 12.62    
  3. 12.3    
  4. 12.7    

Hint:

Median for grouped data  =
M e d i a n space equals space l space plus space open square brackets fraction numerator begin display style n over 2 end style space minus space c over denominator f end fraction close square brackets space cross times space h
w h e r e space l space equals l o w e r space l i m i t space o f space t h e space m e d i a n space c l a s s
n space equals space n u m b e r space o f space o b s e r v a t i o n s
c space equals space c u m u l a t i v e space f r e q u e n c y space o f space t h e space c l a s s space p r e c e d i n g space t h e space m e d i a n space c l a s s space
h space equals space c l a s s space s i z e

The correct answer is: 12.62


     Given : 
    Marks scored by 100 students in a 25 marks unit test of Mathematics is given below 


     Steps to find Median
    Step 1: Find the total number of observations(n) = 100
    Step 2: Define the class size(h), and divide the data into different classes, h = 5
    Step 3: Calculate the cumulative frequency of each class.
    Marks Students Cumulative Frequency
    0-5 10 10
    5-10 18 28
    10-15 42 70
    15-20 23 93
    20-25 7 100
      begin inline style stack sum f subscript i with blank below end style = 100 = n  

    Step 4: Identify the class in which the median falls. (Median Class is the class where n/2 lies.)
    n over 2 space equals space 100 over 2 space equals space 50
F r o m space t h e space a b o v e space t a b l e space 50 space l i e s space i n space t h e space r a n g e space 10 minus 15 comma space T h u s space m e d i a n space c l a s s space i s space 10 minus 15.

    Step 5: Find the lower limit of the median class(l), and the cumulative frequency of the class preceding the median class (c).
    Lower limit of median class (l) = 10
    Cumulative frequency of the class preceding the median class (c) = 28
    Step 6 : Substituting these values in the formula :
    M e d i a n space equals space l space plus space open square brackets fraction numerator begin display style n over 2 end style space minus space c over denominator f end fraction close square brackets space cross times space h
w h e r e space l space equals l o w e r space l i m i t space o f space t h e space m e d i a n space c l a s s
n space equals space n u m b e r space o f space o b s e r v a t i o n s
c space equals space c u m u l a t i v e space f r e q u e n c y space o f space t h e space c l a s s space p r e c e d i n g space t h e space m e d i a n space c l a s s space
h space equals space c l a s s space s i z e
f space equals space f r e q u e n c y space o f space m e d i a n space c l a s s


    M e d i a n space equals space 10 space plus space open square brackets fraction numerator begin display style 100 over 2 end style minus 28 over denominator 42 end fraction close square brackets space cross times space 5 space equals space 12.62

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