The following are the lengths of stay (in days) for a random sample of 21 patients discharged from a particular hospital:

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Draw the histogram for these data using an initial class boundary of 1.5 and a class width of 2 . Note that you can add or remove classes from the figure. Label
each class with its endpoints.

Ask by Lewis Griffin. in the United States

Jan 27,2025

Question

The following are the lengths of stay (in days) for a random sample of 21 patients discharged from a particular hospital:

Send data to calculator
Draw the histogram for these data using an initial class boundary of 1.5 and a class width of 2 . Note that you can add or remove classes from the figure. Label
each class with its endpoints.

Ask by Lewis Griffin. in the United States

Jan 27,2025

UpStudy AI · Accepted Answer

Sure! Let's create a histogram for the provided data with the specified parameters. Since I can't draw the histogram directly here, I'll guide you through the steps and provide a frequency distribution table that you can use to plot the histogram on a calculator or graphing tool.

### **Given Data:**
$$ 13, 9, 5, 11, 6, 3, 12, 10, 11, 7, 3, 2, 2, 2, 10, 10, 12, 12, 8, 8, 4 $$

### **Step 1: Sort the Data**
First, sort the data in ascending order to make it easier to group:
$$ 2, 2, 2, 3, 3, 4, 5, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13 $$

### **Step 2: Define Class Intervals**
- **Initial Class Boundary:** 1.5
- **Class Width:** 2

Using these parameters, the class intervals will be:
1. **1.5 – 3.5**
2. **3.5 – 5.5**
3. **5.5 – 7.5**
4. **7.5 – 9.5**
5. **9.5 – 11.5**
6. **11.5 – 13.5**

*(You can add or remove classes as needed, but these cover all the data points.)*

### **Step 3: Tally the Frequencies**
Count how many data points fall into each class interval.

| **Class Interval (Days)** | **Frequency** |
|---------------------------|---------------|
| 1.5 – 3.5                 | 5             |
| 3.5 – 5.5                 | 2             |
| 5.5 – 7.5                 | 2             |
| 7.5 – 9.5                 | 3             |
| 9.5 – 11.5                | 5             |
| 11.5 – 13.5               | 4             |

**Explanation of Frequencies:**
- **1.5 – 3.5:** Includes 2, 2, 2, 3, 3 → **5** data points
- **3.5 – 5.5:** Includes 4, 5 → **2** data points
- **5.5 – 7.5:** Includes 6, 7 → **2** data points
- **7.5 – 9.5:** Includes 8, 8, 9 → **3** data points
- **9.5 – 11.5:** Includes 10, 10, 10, 11, 11 → **5** data points
- **11.5 – 13.5:** Includes 12, 12, 12, 13 → **4** data points

### **Step 4: Plot the Histogram**
Using the frequency distribution table, you can plot the histogram as follows:

1. **X-Axis (Horizontal):** Represents the **Length of Stay (Days)**. Label each class interval clearly, e.g., "1.5 – 3.5", "3.5 – 5.5", etc.
2. **Y-Axis (Vertical):** Represents the **Frequency** (number of patients).
3. **Bars:** For each class interval, draw a bar whose height corresponds to the frequency.

**Example Layout:**

```
Frequency
|
|                     ____
|        ____        |    |        ____
|        |    |       |    |       |    |       ____
|   ____ |    |   ____|    |   ____|    |   ____|    |
|___|____|____|___|____|____|___|____|____|___|____|____ Length of Stay (Days)
 1.5-3.5 3.5-5.5 5.5-7.5 7.5-9.5 9.5-11.5 11.5-13.5
```

*(Each "____" represents a bar proportional to its frequency. Replace them with actual bar heights based on the frequencies.)*

### **Summary Table for Reference:**

| **Class Interval (Days)** | **Frequency** |
|---------------------------|---------------|
| 1.5 – 3.5                 | 5             |
| 3.5 – 5.5                 | 2             |
| 5.5 – 7.5                 | 2             |
| 7.5 – 9.5                 | 3             |
| 9.5 – 11.5                | 5             |
| 11.5 – 13.5               | 4             |

### **Visualization Tips:**
- **Bar Width:** Each class has the same width of 2 days.
- **Labels:** Clearly label each bar with its corresponding class interval.
- **Scaling:** Ensure the Y-axis is scaled appropriately to accommodate the highest frequency (which is 5 in this case).

You can use graphing software, a graphing calculator, or even Excel to plot this histogram based on the frequency distribution provided.
Here's the histogram for the given data with class boundaries of 1.5 and a class width of 2: - **1.5 – 3.5:** 5 patients - **3.5 – 5.5:** 2 patients - **5.5 – 7.5:** 2 patients - **7.5 – 9.5:** 3 patients - **9.5 – 11.5:** 5 patients - **11.5 – 13.5:** 4 patients

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