8. Construct a histogram from the following frequency distribution on temperatures. (fill in the limits, too). 
Class Limits Class boundaries Frequency 
 28.5–31.5 1 
 31.5–34.5 3 
 34.5–37.5 6 
 37.5–40.5 10 
 40.5–43.5 8 
 43.5–46.5 7

To construct a histogram from the given frequency distribution, we'll start by defining the **class limits**, **class boundaries**, and **frequencies**. The class boundaries are used to avoid gaps between bars in the histogram, and they are typically adjusted slightly from the class limits.

Here's the data as presented, with boundaries:

| **Class Limits** | **Class Boundaries** | **Frequency** |
|------------------|----------------------|---------------|
| 28.5–31.5        | 28.5–31.5            | 1             |
| 31.5–34.5        | 31.5–34.5            | 3             |
| 34.5–37.5        | 34.5–37.5            | 6             |
| 37.5–40.5        | 37.5–40.5            | 10            |
| 40.5–43.5        | 40.5–43.5            | 8             |
| 43.5–46.5        | 43.5–46.5            | 7             |

### Steps to Construct the Histogram:
1. **X-axis**: Use the class boundaries (e.g., 28.5–31.5, 31.5–34.5, etc.) for the x-axis.
2. **Y-axis**: Use the frequencies (1, 3, 6, 10, 8, 7) for the y-axis.
3. **Bars**: Draw rectangular bars for each class boundary interval. The height of each bar corresponds to the frequency for that interval.

Here's a quick guide to help visualize:
- The first bar corresponds to the interval 28.5–31.5 with a height of 1.
- The second bar is for 31.5–34.5 with a height of 3.
- The process continues for all intervals, with the highest bar at the interval 37.5–40.5 (frequency = 10).

Would you like me to create a visual histogram for you?

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**Related Questions:**
1. How do we calculate class width in a frequency distribution?
2. What is the difference between class limits and class boundaries?
3. How can we interpret the shape of a histogram?
4. How does the choice of bin size affect the histogram?
5. Can a histogram be used for categorical data?

**Tip:** When constructing histograms, always ensure there are no gaps between bars by using class boundaries instead of class limits.

8. Construct a histogram from the following frequency distribution on temperatures. (fill in the limits, too). Class Limits Class boundaries Frequency 28.5–31.5 1 31.5–34.5 3 34.5–37.5 6 37.5–40.5 10 40.5–43.5 8 43.5–46.5 7

Learn how to construct a histogram from a frequency distribution of temperatures. This step-by-step guide covers class boundaries, frequencies, and creating visual histograms. Example includes temperature ranges like 28.5–31.5 with frequency 1. Suitable for students in Grades 6-8.

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