Chapter 11.2, Problem 14E

To determine

Make a box-and-whisker plot.

Answer to Problem 14E

Median = $12$

  $Q_1=8$

  $Q_3=14$

Max = $22$

Min = $6$

Explanation of Solution

Given Information: Stem and Leaf plot

Formula Used: Median = ${\left(\frac{n+1}{2}\right)}^{th}term$

Calculation:

Data is $6,7,8,8,9,10,10,12,12,13,14,14,17,21,22$

• Median

Median = ${\left(\frac{n+1}{2}\right)}^{th}term$

So,

Median = ${\left(\frac{15+1}{2}\right)}^{th}term$

Now,

Median = ${\left(8\right)}^{th}term$

As, ${\left(8\right)}^{th}term=12$

Hence,

Median = $12$

• The first quartile, denoted by  $Q_1$, is the median of the lower half of the data set.

Hence,

  $Q_1=8$

• The first quartile, denoted by  $Q_3$, is the median of the upper half of the data set.

Hence,

  $Q_3=14$

• Max = $22$
• Min = $6$