Solved on Jan 20, 2024

Draw a histogram for the lengths of stay (in days) of 19 patients discharged from a hospital, with class boundaries from 1.5 to 13.5 and 6 equal-width classes.

STEP 1

Assumptions
1. The initial class boundary is 1.5.
2. The ending class boundary is 13.5.
3. There are 6 classes of equal width.
4. Each class is labeled with its endpoints.
5. The data set consists of the lengths of stay for 19 patients: $13, 9, 5, 11, 6, 3, 12, 10, 11, 9, 9, 4, 4, 4, 2, 2, 10, 10, 12$

STEP 2

Determine the width of each class by subtracting the initial class boundary from the ending class boundary and then dividing by the number of classes.
$Class\, width = \frac{Ending\, class\, boundary - Initial\, class\, boundary}{Number\, of\, classes}$

STEP 3

Calculate the class width using the given boundaries and number of classes.
$Class\, width = \frac{13.5 - 1.5}{6}$

STEP 4

Compute the class width.
$Class\, width = \frac{12}{6} = 2$

STEP 5

Create the classes using the initial class boundary and the class width. Each class will have a range of 2 units, starting from 1.5 and ending at 13.5.

STEP 6

List the classes with their endpoints:
1. Class 1: 1.5 to 3.5
2. Class 2: 3.5 to 5.5
3. Class 3: 5.5 to 7.5
4. Class 4: 7.5 to 9.5
5. Class 5: 9.5 to 11.5
6. Class 6: 11.5 to 13.5

STEP 7

Tally the number of patient stays that fall into each class.

STEP 8

Count the number of patient stays for Class 1 (1.5 to 3.5).
$Frequency\, for\, Class\, 1 = 4$

STEP 9

Count the number of patient stays for Class 2 (3.5 to 5.5).
$Frequency\, for\, Class\, 2 = 3$

STEP 10

Count the number of patient stays for Class 3 (5.5 to 7.5).
$Frequency\, for\, Class\, 3 = 1$

STEP 11

Count the number of patient stays for Class 4 (7.5 to 9.5).
$Frequency\, for\, Class\, 4 = 4$

STEP 12

Count the number of patient stays for Class 5 (9.5 to 11.5).
$Frequency\, for\, Class\, 5 = 4$

STEP 13

Count the number of patient stays for Class 6 (11.5 to 13.5).
$Frequency\, for\, Class\, 6 = 3$

STEP 14

Draw the histogram using the frequency data for each class. The x-axis will represent the length of stay (in days), and the y-axis will represent the frequency of patient stays. Each bar will represent a class, and the height of the bar will correspond to the frequency of that class.

STEP 15

Label each bar with its class endpoints and ensure that the bars are of equal width and are adjacent to each other with no gaps in between, as this is a histogram for continuous data.

STEP 16

Ensure that the histogram is properly scaled and labeled, with a title that reflects the data being represented.
The histogram is now complete. Each class is represented by a bar, and the height of each bar corresponds to the number of patient stays within that range of days.

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Draw a histogram for the lengths of stay (in days) of 19 patients discharged from a hospital, with class boundaries from 1.5 to 13.5 and 6 equal-width classes.

STEP 1

STEP 2

Determine the width of each class by subtracting the initial class boundary from the ending class boundary and then dividing by the number of classes.
$Class\, width = \frac{Ending\, class\, boundary - Initial\, class\, boundary}{Number\, of\, classes}$

STEP 3

Calculate the class width using the given boundaries and number of classes.
$Class\, width = \frac{13.5 - 1.5}{6}$

STEP 4

Compute the class width.
$Class\, width = \frac{12}{6} = 2$

STEP 5

Create the classes using the initial class boundary and the class width. Each class will have a range of 2 units, starting from 1.5 and ending at 13.5.

STEP 6

List the classes with their endpoints:
1. Class 1: 1.5 to 3.5
2. Class 2: 3.5 to 5.5
3. Class 3: 5.5 to 7.5
4. Class 4: 7.5 to 9.5
5. Class 5: 9.5 to 11.5
6. Class 6: 11.5 to 13.5

STEP 7

Tally the number of patient stays that fall into each class.

STEP 8

Count the number of patient stays for Class 1 (1.5 to 3.5).
$Frequency\, for\, Class\, 1 = 4$

STEP 9

Count the number of patient stays for Class 2 (3.5 to 5.5).
$Frequency\, for\, Class\, 2 = 3$

STEP 10

Count the number of patient stays for Class 3 (5.5 to 7.5).
$Frequency\, for\, Class\, 3 = 1$

STEP 11

Count the number of patient stays for Class 4 (7.5 to 9.5).
$Frequency\, for\, Class\, 4 = 4$

STEP 12

Count the number of patient stays for Class 5 (9.5 to 11.5).
$Frequency\, for\, Class\, 5 = 4$

STEP 13

Count the number of patient stays for Class 6 (11.5 to 13.5).
$Frequency\, for\, Class\, 6 = 3$

STEP 14

Draw the histogram using the frequency data for each class. The x-axis will represent the length of stay (in days), and the y-axis will represent the frequency of patient stays. Each bar will represent a class, and the height of the bar will correspond to the frequency of that class.

STEP 15

Label each bar with its class endpoints and ensure that the bars are of equal width and are adjacent to each other with no gaps in between, as this is a histogram for continuous data.

STEP 16

Ensure that the histogram is properly scaled and labeled, with a title that reflects the data being represented.
The histogram is now complete. Each class is represented by a bar, and the height of each bar corresponds to the number of patient stays within that range of days.

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Draw a histogram for the lengths of stay (in days) of 19 patients discharged from a hospital, with class boundaries from 1.5 to 13.5 and 6 equal-width classes.

STEP 1

STEP 2

STEP 3

Calculate the class width using the given boundaries and number of classes.Class width=13.5−1.56Class\, width = \frac{13.5 - 1.5}{6}Classwidth=613.5−1.5​

STEP 4

Compute the class width.Class width=126=2Class\, width = \frac{12}{6} = 2Classwidth=612​=2

STEP 5

Create the classes using the initial class boundary and the class width. Each class will have a range of 2 units, starting from 1.5 and ending at 13.5.

STEP 6

List the classes with their endpoints:1. Class 1: 1.5 to 3.52. Class 2: 3.5 to 5.53. Class 3: 5.5 to 7.54. Class 4: 7.5 to 9.55. Class 5: 9.5 to 11.56. Class 6: 11.5 to 13.5

STEP 7

Tally the number of patient stays that fall into each class.

STEP 8

Count the number of patient stays for Class 1 (1.5 to 3.5).Frequency for Class 1=4Frequency\, for\, Class\, 1 = 4FrequencyforClass1=4

STEP 9

Count the number of patient stays for Class 2 (3.5 to 5.5).Frequency for Class 2=3Frequency\, for\, Class\, 2 = 3FrequencyforClass2=3

STEP 10

Count the number of patient stays for Class 3 (5.5 to 7.5).Frequency for Class 3=1Frequency\, for\, Class\, 3 = 1FrequencyforClass3=1

STEP 11

Count the number of patient stays for Class 4 (7.5 to 9.5).Frequency for Class 4=4Frequency\, for\, Class\, 4 = 4FrequencyforClass4=4

STEP 12

Count the number of patient stays for Class 5 (9.5 to 11.5).Frequency for Class 5=4Frequency\, for\, Class\, 5 = 4FrequencyforClass5=4

STEP 13

Count the number of patient stays for Class 6 (11.5 to 13.5).Frequency for Class 6=3Frequency\, for\, Class\, 6 = 3FrequencyforClass6=3

STEP 14

Draw the histogram using the frequency data for each class. The x-axis will represent the length of stay (in days), and the y-axis will represent the frequency of patient stays. Each bar will represent a class, and the height of the bar will correspond to the frequency of that class.

STEP 15

Label each bar with its class endpoints and ensure that the bars are of equal width and are adjacent to each other with no gaps in between, as this is a histogram for continuous data.

STEP 16

Ensure that the histogram is properly scaled and labeled, with a title that reflects the data being represented.The histogram is now complete. Each class is represented by a bar, and the height of each bar corresponds to the number of patient stays within that range of days.

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Calculate the class width using the given boundaries and number of classes.
$Class\, width = \frac{13.5 - 1.5}{6}$

Compute the class width.
$Class\, width = \frac{12}{6} = 2$

List the classes with their endpoints:
1. Class 1: 1.5 to 3.5
2. Class 2: 3.5 to 5.5
3. Class 3: 5.5 to 7.5
4. Class 4: 7.5 to 9.5
5. Class 5: 9.5 to 11.5
6. Class 6: 11.5 to 13.5

Count the number of patient stays for Class 1 (1.5 to 3.5).
$Frequency\, for\, Class\, 1 = 4$

Count the number of patient stays for Class 2 (3.5 to 5.5).
$Frequency\, for\, Class\, 2 = 3$

Count the number of patient stays for Class 3 (5.5 to 7.5).
$Frequency\, for\, Class\, 3 = 1$

Count the number of patient stays for Class 4 (7.5 to 9.5).
$Frequency\, for\, Class\, 4 = 4$

Count the number of patient stays for Class 5 (9.5 to 11.5).
$Frequency\, for\, Class\, 5 = 4$

Count the number of patient stays for Class 6 (11.5 to 13.5).
$Frequency\, for\, Class\, 6 = 3$

Ensure that the histogram is properly scaled and labeled, with a title that reflects the data being represented.
The histogram is now complete. Each class is represented by a bar, and the height of each bar corresponds to the number of patient stays within that range of days.