Question

Which choice below is a boxplot for the following distribution? 67, 66, 64, 62, 60, 56, 54, 50, 46, 42, 41, 40, 40, 38, 35, 21, 19

Answer 1

Answer: Box plot E

Explanation:

A P E X

Answer 2

Option E - Box plot E

Explanation:

Given : Data,

67, 66, 64, 62, 60, 56, 54, 50, 46, 42, 41, 40, 40, 38, 35, 21, 19

To find : Which choice below is a boxplot for the following distribution?

Solution :

Step 1- Arranging the data from lowest to highest,

{19,21,35,38,40,40,41,42,46,50,54,56,60,62,64,66,67}

Step 2 - Find the median of the data

As the data is odd numbers so the median is
`(n+1)/(2)` th term.

`(n+1)/(2)=(17+1)/(2)=9th` term.

9th term is 46

∴
`Q_2=46`

Step 3 - To find Upper quartile and lower quartile

Lower quartile data set is the median of the upper terms from median

{19,21,35,38,40,40,41,42}

Median of the set is
`M=(38+40)/(2)=39`

∴
`Q_1=39`

Upper quartile data set is the median of the lower terms from median

{ 50,54,56,60,62,64,66,67}

Median of the set is
`M=(60+62)/(2)=61`

∴
`Q_3=61`

We have plot the box plot attached below.

Our box plot is matched with Box plot E.

Therefore, Option E is correct.