Chapter B.2, Problem 43E

(a).

To determine

To calculate:

Lower and upper quartile for the given data.

Answer to Problem 43E

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

Explanation of Solution

Given information:

Data: $\text{46},\text{48},\text{48},\text{5}0,\text{52},\text{47},\text{51},\text{47},\text{49},\text{53}$

Calculation:

At first write the given data in numerical order:

  $46,47,47,48,48,49,50,51,52,53$

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,

  $\begin{array}{l}\frac{48+49}{2}\\ =48.5\end{array}$

So the median of the given data set is $48.5$ .

The median of the four numbers that are less than $48.5$ is $47$ , while the median of the four numbers that are greater than $48.5$ is $51$

Since the $n$ is even.

So, lower quartile Is $47$ and upper quartile is $51$ .

(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 $46$ , the lower quartile as $47$ , the median as

  $48.5$ , the upper quartile as $51$ and the largest number as $53$ .