Chapter 13.2, Problem 37E

To determine

To find: The lower and upper quartiles and to sketch a box-and-whisker plot for given data set.

Answer to Problem 37E

The lower quartile is $11$ and the upper quartile is $16$ .

Explanation of Solution

Given information:

Given data set is:

  $11,10,11,14,17,16,14,11,8,14,20.$

Calculation:

Let us order the given data. So, the ordered data is:

  $8,10,11,11,11,14,14,14,16,17,20.$

Median $=14$

The median of the five numbers that are less than $14$ is $11$ .

So, the lower quartile is $11$ .

The median of the five numbers that are greater than $14$ is $16$ .

So, the upper quartile is $16$ .

Box-and-whisker plot:

Plotting the least number $8$, the lower quartile $11$ , the median $14$ , the upper quartile $16$ and the greatest number $20$ , the box-and-whisker plot is: