https://file.aiquickdraw.com/mathbot/file/1729229433752zcagie46.jpg

To construct the histogram as requested in the problem:

### Step 1: Determine the Class Width
You are given an initial class boundary of 13.5, an ending class boundary of 48.5, and 5 classes of equal width. To find the class width:
\[
\text{Class width} = \frac{48.5 - 13.5}{5} = \frac{35}{5} = 7
\]
So, each class will have a width of 7 units.

### Step 2: Define the Class Intervals
Starting with the initial boundary of 13.5, the intervals for the 5 classes will be:
1. 13.5 - 20.5
2. 20.5 - 27.5
3. 27.5 - 34.5
4. 34.5 - 41.5
5. 41.5 - 48.5

### Step 3: Tally the Frequencies
The data is:  
19, 15, 43, 39, 35, 31, 27, 22, 18, 14, 42, 38, 21, 21, 17, 17, 17, 17.

Now, count how many values fall into each interval:

1. **13.5 - 20.5**: 19, 15, 18, 14, 17, 17, 17, 17 → 8 values
2. **20.5 - 27.5**: 27, 22, 21, 21 → 4 values
3. **27.5 - 34.5**: 31 → 1 value
4. **34.5 - 41.5**: 39, 35, 38 → 3 values
5. **41.5 - 48.5**: 43, 42 → 2 values

### Step 4: Draw the Histogram
Using the calculated frequencies:

- 13.5 - 20.5: Frequency = 8
- 20.5 - 27.5: Frequency = 4
- 27.5 - 34.5: Frequency = 1
- 34.5 - 41.5: Frequency = 3
- 41.5 - 48.5: Frequency = 2

You can now create the histogram by plotting the class intervals on the x-axis and the corresponding frequencies on the y-axis.

Would you like further clarification or details on any part of this solution?

### Follow-up Questions:
1. What is the significance of class boundaries in a histogram?
2. How would you calculate the midpoint of each class?
3. What is the difference between a frequency distribution and a relative frequency distribution?
4. How would the histogram change if the class width was larger?
5. How can we estimate the median from a histogram?

**Tip:** Always ensure the intervals do not overlap, and that every data point is counted exactly once.

Below are the times (in days) it takes for a sample of 18 customers from Jack's computer store to pay their invoices. Draw the histogram for these data using an initial class boundary of 13.5, an ending class boundary of 48.5, and 5 classes of equal width. Label each class with its endpoints.

Learn how to draw a histogram using data of invoice payment times from 18 customers, with steps to determine class width, define intervals, and calculate frequencies. This example covers core statistical concepts and data visualization techniques suitable for Grades 10-12.

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