Question

vi): Prove that:
P50=D5=Q2=median.

Answer 1

Answer:

It is fundamental concept that Median, second quartile, 5th decile and 50th percentile are same.

i.e M=Q2=D5=P50   

Answer 2

Proof:

P50 =$[\frac{50(N+1)}{100} ]$th term

D5 =$[\frac{5(N+1)}{10} ]$th term

Q2=$[\frac{2(N+1)}{4}]$th term

Median =$(\frac{N+1}{2} )$th term

By simplifying the formulas,we get:-

P50 =$(\frac{N+1}{2} )$th term

D5 =$(\frac{N+1}{2} )$th term

Q2 =$(\frac{N+1}{2} )$th term

Median =$(\frac{N+1}{2} )$th term

Therefore:- P50=D5=Q2=Median