What is the deivation of the formulae for finding median and mode of grouped data? (as listed in class 10 mathematics book)

Asked by reetatyagi8 | 6th Aug, 2015, 10:07: AM

Expert Answer:

Derivation of Mode formula for grouped data:
 
Let the frequency of the modal class be f1. Frequency of the class just before modal class be f0 and frequency of the class just after the modal class be f2.
if the lower limit of the modal class is l0, then mode is given by l0+x as shown in the figure.
 
F r o m space t h e space f i g u r e comma space increment A E B tilde increment D E C rightwards double arrow fraction numerator A B over denominator C D end fraction equals fraction numerator B E over denominator D E end fraction equals fraction numerator f subscript 1 minus f subscript 0 over denominator f subscript 1 minus f subscript 2 end fraction increment B E F tilde increment B D C rightwards double arrow fraction numerator F E over denominator B C end fraction equals fraction numerator B E over denominator B D end fraction equals fraction numerator f subscript 1 minus f subscript 0 over denominator open parentheses f subscript 1 minus f subscript 0 close parentheses plus open parentheses f subscript 1 minus f subscript 2 close parentheses end fraction equals fraction numerator f subscript 1 minus f subscript 0 over denominator 2 f subscript 1 minus f subscript 0 minus f subscript 2 end fraction rightwards double arrow F E equals fraction numerator f subscript 1 minus f subscript 0 over denominator 2 f subscript 1 minus f subscript 0 minus f subscript 2 end fraction cross times B C equals open parentheses fraction numerator f subscript 1 minus f subscript 0 over denominator 2 f subscript 1 minus f subscript 0 minus f subscript 2 end fraction close parentheses f subscript 1 rightwards double arrow x equals open parentheses fraction numerator f subscript 1 minus f subscript 0 over denominator 2 f subscript 1 minus f subscript 0 minus f subscript 2 end fraction close parentheses f subscript 1  H e n c e comma space m o d e equals l subscript 0 plus x equals l subscript 0 plus open parentheses fraction numerator f subscript 1 minus f subscript 0 over denominator 2 f subscript 1 minus f subscript 0 minus f subscript 2 end fraction close parentheses f subscript 1 space left parenthesis P r o v e d right parenthesis

Answered by satyajit samal | 7th Aug, 2015, 09:10: AM

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