The following are the lengths of stay (in days) for a random sample of 21 patients discharged from a particular hospital: \[ 13,9,5,11,6,3,12,10,11,7,3,2,2,2,10,10,12,12,8,8,4 \] 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.

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.