Question

sons in the NHL,nts than anyone whoccomplished thiser games thanHer. Here are theRg each season:74, 45, 81, 48, 80,Working for a Living The following data represent the num-ber of hours worked per week for a random sample of 15adults in the United States and Canada, based on data froman August 2004 study by the Gallup Organization.USA2641537049661446464034334435uen-atedinedion.38Canada423536223949633140354068315328(a) Create a side-by-side boxplot of the data.

Answer 1

Step 1:

In descriptive statistics, a box plot or boxplot (also known as box and whisker plot) is a type of chart often used in explanatory data analysis. Box plots visually show the distribution of numerical data and skewness through displaying the data quartiles (or percentiles) and averages.

Step 2:

To sketch a boxplot, you will need to determine the following:

Minimum

Lower quartile

Median

Upper quartile

Maximum

Step 3:

USA

First arrange the data from the least to the greatest.

14 , 26, 33, 34, 35, 38, 40, 41, 44, 46, 46, 49, 53, 66, 70.

Minimum = 14

$\begin{gathered} \text{Lower quartile position = }\frac{1}{4}(n+1)^{th} \\ \text{= }\frac{15+1}{4}\text{ = }\frac{16}{4}=4^{th} \\ Q_1\text{ = lower quartile = 34} \end{gathered}$

Median = 41

$\begin{gathered} \text{Upper quartile position = }\frac{3}{4}(n+1)^{th} \\ =\text{ }\frac{3\text{ }\times(15+1)}{4} \\ =12^{th} \\ Q_3\text{ = upper quartile = 49} \end{gathered}$

Maximum = 70

Interquartile range IQR = 49 - 34 = 15

Canada

22, 28, 31, 31, 35, 35, 36, 39, 40, 40, 42, 49, 53, 63, 68

Minimum = 22

$\begin{gathered} Q1\text{ Position = }\frac{(n+1)^{th}\text{ }}{4}\text{ = }\frac{16}{4}th=4^{th} \\ Q_1\text{ = 31} \end{gathered}$

Median = 39

$\begin{gathered} UpperquartileQ_{_3\text{ }}\text{ = 49} \\ \end{gathered}$

Maximum = 68

Interquartile range = 49 - 31 = 18