Maths-
General
Easy

Question

The median of the following data is

  1. 134.5    
  2. 144.5    
  3. 154.5    
  4. 140.5    

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 minus c over denominator f end fraction close square brackets cross times h
w h e r e space comma
l space 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 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 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
f equals space f r e q u e n c y space o f space t h e 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: 144.5


     Given :


    Steps to find median 
    Step 1 : Fix the class interval by subtracting 0.5 from lower limit and adding 0.5 to the upper limit of each interval
    Class Interval Frequency
    109.5 - 119.5 5
    119.5 - 129.5 25
    129.5 - 139.5 40
    139.5 - 149.5 60
    149.5 - 159.5 40
    159.5 - 169.5 25
    169.5 - 179.5 5
      n = 200

    Step 2: Find the total number of observations(n) = 200
    Step 3: Define the class size(h), and divide the data into different classes = 10
    Step 4: Calculate the cumulative frequency of each class.
    Class Interval Frequency Cumulative Frequency
    109.5 - 119.5 5 5
    119.5 - 129.5 25 30
    129.5 - 139.5 40 70
    139.5 - 149.5 60 130
    149.5 - 159.5 40 170
    159.5 - 169.5 25 195
    169.5 - 179.5 5 200
      n = 200

     

    Step 5: Identify the class in which the median falls. (Median Class is the class where n/2 lies.)
    Median class = n over 2 space equals space 200 over 2 space equals space 100
    Thus the median class is 139.5 - 149.5
    Step 6: Find the
    lower limit of the median class(l) =  139.5,
    and the cumulative frequency of the class preceding the median class (c) = 70
    Now, use the following formula to find the median value.

    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 minus c over denominator f end fraction close square brackets cross times h
w h e r e space comma
l space 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 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 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
f equals space f r e q u e n c y space o f space t h e 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

    M e d i a n space equals space 139.5 space plus space open square brackets fraction numerator begin display style 200 over 2 minus 70 end style over denominator 60 end fraction close square brackets cross times 10 space equals 144.5

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