Chapter B.2, Problem 44E

(a).

To determine

To calculate:

Lower and upper quartile for the given data.

Answer to Problem 44E

Lower and upper quartile for the given data is $13,21.5$

Explanation of Solution

Given information:

Data: $\text{25},\text{2}0,\text{22},\text{28},\text{24},\text{28},\text{25},\text{19},\text{27},\text{29},\text{28},\text{21}$

Calculation:

At first write the given data in numerical order:

  $19,20,21,22,24,25,25,27,28,28,28,29$

The median of $n$ numbers when $n$ is odd, is the mid number when the numbers are written in numerical order.

In case $n$ is even, and then the median is the average of two middle numbers.

Median is,

  $\begin{array}{l}\frac{25+25}{2}\\ =25\end{array}$

So the median of the given data set is $25$ .

The median of the four numbers that are less than $25$ is $21$ , while the median of the four numbers that are greater than $25$ is $28$

Since the $n$ is even.

So, lower quartile is $21$ and upper quartile is $28$ .

(b).

To determine

To graph:

Box and whisker plot for the given data.

Explanation of Solution

Given information:

Data: $\text{25},\text{2}0,\text{22},\text{28},\text{24},\text{28},\text{25},\text{19},\text{27},\text{29},\text{28},\text{21}$

Graph:

  

Interpretation:

For the given data, Box and whisker plot is as above.

In which,

The above graph has the smallest number as $19$ , the lower quartile as $21$ , the median as

  $25$ , the upper quartile as $28$ and the largest number as $29$ .