Question

the following are distances (in miles) traveled to the workplace by 23 employees of a certain hospital. 7, 2, 37, 32, 27, 22, 16, 11, 6, 1, 36, 31, 25, 20, 15, 10, 5, 24, 24, 9, 9, 9, 14 send data to calculator draw the histogram for these data using an initial class boundary of 0.5, an ending class boundary of 45.5, and 5 classes of equal width. note that you can add or remove classes from the figure. label each class with its endpoints. frequency 0 0 0 0 0 distance (in miles)

Explanation:

Step1: Calculate class - width

The range of data is from the minimum value to the maximum value. The minimum value in the data set is 1 and the maximum is 37. The class - width $w$ is calculated as $\frac{\text{ending class boundary}-\text{initial class boundary}}{\text{number of classes}}$. Here, the initial class boundary is $0.5$, the ending class boundary is $45.5$ and the number of classes is 5. So, $w=\frac{45.5 - 0.5}{5}=\frac{45}{5}=9$.

Step2: Define class intervals

The first class interval with an initial class boundary of $0.5$ is $0.5 - 9.5$, the second is $9.5 - 18.5$, the third is $18.5 - 27.5$, the fourth is $27.5 - 36.5$ and the fifth is $36.5 - 45.5$.

Step3: Count frequencies

For the class $0.5 - 9.5$: The values in this class are 1, 6, 5, 9, 9, 9. So the frequency $f_1 = 6$.
For the class $9.5 - 18.5$: The values are 11, 10, 14, 16. So the frequency $f_2 = 4$.
For the class $18.5 - 27.5$: The values are 20, 22, 25, 24, 24, 27. So the frequency $f_3 = 6$.
For the class $27.5 - 36.5$: The values are 31, 32, 36. So the frequency $f_4 = 3$.
For the class $36.5 - 45.5$: The value is 37. So the frequency $f_5 = 1$.

Step4: Draw the histogram

On the x - axis, label the class intervals ($0.5 - 9.5$, $9.5 - 18.5$, $18.5 - 27.5$, $27.5 - 36.5$, $36.5 - 45.5$) and on the y - axis, label the frequency. Draw rectangles for each class interval with height equal to the frequency of that class.

Answer:

The class intervals and their frequencies are:

Class Interval	Frequency
$9.5 - 18.5$	4
$18.5 - 27.5$	6
$27.5 - 36.5$	3
$36.5 - 45.5$	1