Question

the following are the lengths of stay (in days) for a random sample of 19 patients discharged from a particular hospital: 13, 9, 5, 11, 6, 3, 12, 10, 11, 9, 9, 9, 4, 4, 4, 2, 2, 10, 10. send data to calculator. draw the histogram for these data using an initial class boundary of 1.5, an ending class boundary of 13.5, and 6 classes of equal width. note that you can add or remove classes from the figure. label each class with its endpoints.

Explanation:

Step1: Calculate class - width

The formula for class - width $w=\frac{\text{ending class boundary}-\text{initial class boundary}}{\text{number of classes}}$. Here, the initial class boundary is $1.5$, the ending class boundary is $13.5$, and the number of classes is $6$. So, $w = \frac{13.5 - 1.5}{6}=\frac{12}{6}=2$.

Step2: Determine class intervals

The first class starts at $1.5$. The class intervals are:

• Class 1: $1.5 - 3.5$
• Class 2: $3.5 - 5.5$
• Class 3: $5.5 - 7.5$
• Class 4: $7.5 - 9.5$
• Class 5: $9.5 - 11.5$
• Class 6: $11.5 - 13.5$

Step3: Count frequencies

For the class $1.5 - 3.5$, the values $2,2,3$ fall in this class, so the frequency $f_1 = 3$.
For the class $3.5 - 5.5$, the value $5$ falls in this class, so the frequency $f_2 = 1$.
For the class $5.5 - 7.5$, the value $6$ falls in this class, so the frequency $f_3 = 1$.
For the class $7.5 - 9.5$, the values $9,9,9,9$ fall in this class, so the frequency $f_4 = 4$.
For the class $9.5 - 11.5$, the values $10,10,11,11$ fall in this class, so the frequency $f_5 = 4$.
For the class $11.5 - 13.5$, the values $12,13$ fall in this class, so the frequency $f_6 = 2$.

Step4: Draw the histogram

On the x - axis, label the class intervals with their endpoints ($1.5 - 3.5$, $3.5 - 5.5$, $5.5 - 7.5$, $7.5 - 9.5$, $9.5 - 11.5$, $11.5 - 13.5$). On the y - axis, label the frequencies. Draw rectangles with heights corresponding to the frequencies for each class interval.

Answer:

The histogram has class intervals $1.5 - 3.5$ with frequency $3$, $3.5 - 5.5$ with frequency $1$, $5.5 - 7.5$ with frequency $1$, $7.5 - 9.5$ with frequency $4$, $9.5 - 11.5$ with frequency $4$, $11.5 - 13.5$ with frequency $2$.