Chapter 13.2, Problem 38E

To determine

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

Answer to Problem 38E

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

Explanation of Solution

Given information:

Given data set is:

  $46,48,48,50,52,47,51,47,49,53.$

Calculation:

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

  $46,47,47,48,48,49,50,51,52,53.$

Median $\frac{48+49}{2}=48.5$

The median of the five numbers that are less than $48.5$ is $47$ .

So, the lower quartile is $47$ .

The median of the six numbers that are greater than $48.5$ is $51$ .

So, the upper quartile is $51$ .

Box-and-whisker plot:

Plotting the least number $46$, the lower quartile $47$ , the median $48.5$ , the upper quartile $51$ and the greatest number53, the box-and-whisker plot is: