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    Maths-
    General
    Easy

    Question

    The median of the following frequency distribution

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

    hintHint:

    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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