archie is fed up with waiting in line at his local post office and decides to take action. over the course…

archie is fed up with waiting in line at his local post office and decides to take action. over the course of the next few months, he records the waiting times for each of a random selection of 18 post - office visits made by him and other customers. these waiting times (in minutes) are as follows. 5, 18, 25, 13, 11, 7, 24, 20, 11, 18, 22, 27, 14, 12, 26, 9, 8, 23 send data to calculator using the tool provided, construct a box - and - whisker plot (sometimes called a boxplot) for the data.

archie is fed up with waiting in line at his local post office and decides to take action. over the course of the next few months, he records the waiting times for each of a random selection of 18 post - office visits made by him and other customers. these waiting times (in minutes) are as follows. 5, 18, 25, 13, 11, 7, 24, 20, 11, 18, 22, 27, 14, 12, 26, 9, 8, 23 send data to calculator using the tool provided, construct a box - and - whisker plot (sometimes called a boxplot) for the data.

Answer

Explanation:

Step1: Sort the data

$5,7,8,9,11,11,12,13,14,18,18,20,22,23,24,25,26,27$

Step2: Find the minimum

The minimum value is $5$.

Step3: Find the first - quartile ($Q_1$)

There are $n = 18$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{18+1}{4}=4.75$. So, $Q_1=9+(11 - 9)\times0.75 = 10.5$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n+1}{2}=\frac{18 + 1}{2}=9.5$. So, $Q_2=\frac{14 + 18}{2}=16$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(18+1)}{4}=14.25$. So, $Q_3=23+(24 - 23)\times0.25=23.25$.

Step6: Find the maximum

The maximum value is $27$.

Step7: Construct the box - and - whisker plot

Draw a number line that includes the range from $5$ to $27$. Mark the minimum ($5$) with a dot on the left - hand side, $Q_1 = 10.5$, the median $Q_2=16$, $Q_3 = 23.25$, and the maximum ($27$) with dots. Draw a box from $Q_1$ to $Q_3$ and a vertical line inside the box at the median. Draw whiskers from the box to the minimum and maximum values.

Answer:

The box - and - whisker plot has a minimum of $5$, $Q_1 = 10.5$, median of $16$, $Q_3=23.25$, and a maximum of $27$.