Chapter B.2, Problem 42E

(a).

To determine

To calculate:

Lower and upper quartile for the given data.

Answer to Problem 42E

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

Explanation of Solution

Given information:

Data: $\text{11},\text{1}0,\text{11},\text{14},\text{17},\text{16},\text{14},\text{11},\text{8},\text{14},\text{2}0$

Calculation:

At first write the given data in numerical order:

  $8,10,11,11,11,14,14,14,16,17,20$

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.

So the median of the given data set is $14$ .

The median of the four numbers that are to the left of $14$ is $\frac{11+11}{2}=11$

Since the $n$ is even.

So, lower quartile Is $11$ the median of four numbers that are to the right of $14$ is $16$ .

So upper quartile is $16$ .

(b).

To determine

To graph:

Box and whisker plot for the given data.

Explanation of Solution

Given information:

Data: $\text{11},\text{1}0,\text{11},\text{14},\text{17},\text{16},\text{14},\text{11},\text{8},\text{14},\text{2}0$

Graph:

  

Interpretation:

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

In which,

The above graph has the smallest number as $8$ , the lower quartile as $11$ , the median as

  $14$ , the upper quartile as $16$ and the largest number as $20$ .