https://file.aiquickdraw.com/mathbot/file/1728445135646ohby0gmm.jpg

Let's analyze the histogram and answer the given questions.

### (a) Determine the number of classes.
Each bar in a histogram represents a class interval. By looking at the histogram, we see six bars. Therefore, there are **6 classes**.

### (b) Estimate the greatest and least frequencies.
- The **greatest frequency** corresponds to the tallest bar, which is at around **300**.
- The **least frequency** corresponds to the shortest bar, which is at around **50**.

### (c) Determine the class width.
To find the class width, we subtract the lower limit of one class from the lower limit of the next class. From the x-axis labels:
- The class limits are: 34.5, 44.5, 54.5, 64.5, 74.5, 84.5, 94.5.
- The class width is \( 44.5 - 34.5 = 10 \).

Thus, the **class width is 10** thousand dollars.

### (d) Describe any patterns with the data.
The histogram appears to be **approximately symmetric** with a peak in the middle. Most employees earn salaries between 54.5k and 74.5k, with the highest frequency near the middle of the distribution. The frequencies taper off towards both lower and higher salary ranges, indicating fewer employees earn extremely low or high salaries.

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Would you like more details or have any other questions? 

Here are 5 related questions:
1. How can the histogram shape be classified (e.g., skewed, symmetric)?
2. How do you compute relative frequency from this histogram?
3. What is the cumulative frequency, and how could it be derived from this data?
4. How would increasing the number of classes affect the histogram?
5. How can the mean salary be estimated from the histogram?

**Tip**: When reading histograms, always check the class intervals and the scale on the y-axis to accurately interpret frequencies.

Use the frequency histogram to complete the following parts: (a) Determine the number of classes. (b) Estimate the greatest and least frequencies. (c) Determine the class width. (d) Describe any patterns with the data.

Learn how to analyze a frequency histogram to determine the number of classes, estimate frequencies, calculate class width, and observe data patterns. This example examines employee salary data, highlighting key statistical concepts.

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