Maths-
General
Easy

Question

The median from the following data is

  1. 153.79    
  2. 153.91    
  3. 165.18    
  4. 165.93    

hintHint:

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 cross times h comma space w h e r e
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 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 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
f equals space 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: 153.79


     Given :

     
     Step 1 : Find class interval  and cumulative frequency

    Mid Value Class Interval Frequency Cumulative Frequency
    115 110-120 6 6
    125 120-130 25 31
    135 130-140 48 79
    145 140-150 72 151
    155 150-160 116 267
    165 160-170 60 327
    175 170-180 38 365
    185 180-190 22 387
    195 190-200 3 390
        n = 390  

    Step 2: Find median class
     M e d i a n space c l a s s space equals n over 2 space equals space 390 over 2 space equals space 195
T h u s comma space m e d i a n space c l a s s space equals space 150 minus 160

    Step 3: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 space minus space c over denominator f end fraction close square brackets cross times h comma space w h e r e
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 150
n space equals space 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 390
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 equals 151
f equals space 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 116
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 150 plus space open square brackets fraction numerator begin display style 195 space minus space 151 end style over denominator 116 end fraction close square brackets cross times 10 space equals space 153.79

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