Question

Find the Quartile Deviation for the following set of data:
$490,540,590,600,620,650,680,770,830,840,890,900$

• A. $12$
• B. $122.5$
• C. $13$
• D. $12.6$

Answer 1

Answer: (B)

$122.5$

$490,540,590,600,620,650,680,770,830,840,890,900$

$Q_d=\frac{Q_3-Q_1}{2}$

$Q_d\to$ Quality deviation

$Q_1\to {25}^{th}$ perentile

$Q_3\to {75}^{th}$ perentile

$Q_1=\left(\frac{n+1}{4}\right)$th term

$=\frac{13}{4}$th term

$=3.25$th term

$=3^{rd}$ term$+0.25\times (4^{th}$ term$-3^{rd}$ term$)$

$=590+0.25\times (600-590)$

$=590+0.25\times 10$

$Q_1=592.5$

$Q_3=\frac{3(n+1)}{4}$th term

$=\frac{3}{4}\times 13={9.75}^{th}$ term

$=9^{th}$ term$+0.75\times ({10}^{th}$ term$-9^{th}$ term$)$

$=830+0.75\times (840-830)$

$=830+7.5$

$Q_3=837.5$

$Q_d=\frac{Q_3-Q_1}{2}$

$=\frac{837.5-592.5}{2}=\frac{245}{2}=122.5$.