Let P, Q, R represent mean, median and mode. If for some distribution 5 P=4 Q=(R)/(2) , then what is (P+Q)/(2 P+0.7 R) equal to?

Correct answer: D. (1)/(4) 5 P=4 Q=(R)/(2)=kP=(k)/(5), Q=(k)/(4), R=2 k (P+Q)/(2 P+0.7 R)=((k)/(5)+(k)/(4))/((2 k)/(5)+0.7(2 k))=(k((1)/(5)+(1)/(4)))/(k((2)/(5)+(7)/(5)))=((9)/(20))/((9)/(5))=(1)/(4)

NDA 2023

Exam: NDA
Year: 2023
Subject: Mathematics
Chapter: Statistics

NDA 2023 · Mathematics · Statistics

Let P, Q, R represent mean, median and mode. If for some...

Let

P, Q, R

represent mean, median and mode. If for some distribution

5 P=4 Q=\frac{R}{2}

, then what is

\frac{P+Q}{2 P+0.7 R}

equal to?

Options

A $\frac{1}{12}$
B $\frac{1}{7}$
C $\frac{2}{9}$
D $\frac{1}{4}$

Correct answer

D. $\frac{1}{4}$

Step-by-step solution

5 P=4 Q=\frac{R}{2}=kP=\frac{k}{5}, Q=\frac{k}{4}, R=2 k\therefore \quad \frac{P+Q}{2 P+0.7 R}=\frac{\frac{k}{5}+\frac{k}{4}}{\frac{2 k}{5}+0.7(2 k)}=\frac{k\left(\frac{1}{5}+\frac{1}{4}\right)}{k\left(\frac{2}{5}+\frac{7}{5}\right)}=\frac{\frac{9}{20}}{\frac{9}{5}}=\frac{1}{4}

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