Maths-
General
Easy

Question

The median of the following frequency distribution

  1. 45    
  2. 45.75    
  3. 46    
  4. 46.75    

Hint:

Median formula :
l space plus space open square brackets fraction numerator begin display style n over 2 end style space minus c over denominator f end fraction close square brackets cross times h

w h e r e comma space
l space equals space 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 t o t a l space n u m b e r space o f space o b s e r v a t i o n s
c equals space 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
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
h space equals space c l a s s space s i z e

The correct answer is: 46.75


     Given :

    Step 1: Find the total number of observations(n), cumulative frequency(cf)
    Wages  No. of workers Cumulative frequency
    20-30 3 3
    30-40 5 8
    40-50 20 28
    50-60 10 38
    60-70 5 43
      n = 43  

    Step 2 : Find median class
    M e d i a n space c l a s s space equals fraction numerator n space over denominator 2 end fraction space equals space fraction numerator 43 space over denominator 2 end fraction space equals 21.5
T h u s comma space m e d i a n space c l a s s space l i e s space b e t w e e n space 40 minus 50

    Step 3: Use the following formula to find the median value.
    l space plus space open square brackets fraction numerator begin display style n over 2 end style space minus c over denominator f end fraction close square brackets cross times h

w h e r e comma space
l space equals space 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 space equals space 40
n space equals space t o t a l space n u m b e r space o f space o b s e r v a t i o n s space equals space 43
c equals space 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 equals space 8 space
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 space equals space 20
h space equals space c l a s s space s i z e space equals space 10

    M e d i a n space equals space 40 space plus space open square brackets fraction numerator begin display style 21.5 space minus 8 end style over denominator 20 end fraction close square brackets cross times 10 space equals space 46.75

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