Question

Match the following for the even-numbered data set.

12

19

17

15

20

25

29

18

16

30

• A. 30
• B. 18.5
• C. 16
• D. 9

Answer 1

After arranging the provided data set in an ascending order, we get

$12$

$15$

$16$

$17$

$18$

$19$

$20$

$25$

$29$

$30$

$\bullet$ Upper extreme is the highest data point, i.e., 30

$\bullet$ Middle quartile= median of the whole data set= mean of $18$ and $19$

$\Rightarrow \text{Middle quartile}=\frac{18+19}{2}=\frac{37}{2}=18.5$

$\bullet$ To find the lower quartile, we need to consider the left part of middle quartile $\left(18.5\right)$ of the arranged data set.

$12$

$15$

$\underset{–}{16}$

$17$

$18$

Lower quartile= median of $\{12,15,16,17,18\}$

$\Rightarrow \text{Lower quartile}=16$

$\bullet$ Inter-quartile range is the difference between the upper and the lower quartiles.

To find the upper quartile, we need to consider the right part of middle quartile $\left(18.5\right)$ of the arranged data set.

$19$

$20$

$25$

$29$

$30$

Upper quartile = Median of $\{19,20,25,29,30\}$

$\Rightarrow \text{Upper quartile}=25$

$\therefore \text{Inter-quartile range}$
$=\text{Upper quartile}-\text{Lower quartile}$
$=25-16=9$