https://file.aiquickdraw.com/mathbot/file/17264463333341tewfjjh.jpg

Let's analyze the histogram and answer the questions based on the image:

### (a) **Determine the number of classes.**
- Looking at the histogram, the salary ranges on the x-axis are divided into intervals: 32, 37, 42, 47, 52, 57, 62 (in thousands).
- Each interval represents a class, and there are **6 intervals** visible (32-37, 37-42, 42-47, 47-52, 52-57, 57-62).

Thus, there are **6 classes**.

### (b) **Estimate the greatest and least frequencies.**
- The y-axis represents frequency, and the highest bar has a frequency of approximately **300**.
- The smallest frequency is represented by the smallest bars, which have a frequency of about **50**.

So, the least frequency is about **50**, and the greatest frequency is about **300**.

### (c) **Determine the class width.**
- The class width is the difference between the upper and lower boundaries of each class.
- For example, one class is from 32 to 37, which means the class width is $ 37 - 32 = 5 $.

Thus, the class width is **5**.

### (d) **Describe any patterns with the data.**
- The histogram shows that most employee salaries fall between **$40,000 and $49,000**.
- The frequency decreases as you move towards both ends (salaries below $35,000 and above $60,000).
  
### Answer to Multiple Choice:
- **C.** About half of the employees' salaries are between **$40,000 and $49,000**.

Would you like any further details on these calculations or have any questions?

### Related Questions:
1. How would the pattern change if the histogram was skewed to the left or right?
2. What can be inferred about the median salary from this histogram?
3. How could outliers in salary impact this histogram?
4. What would happen to the histogram if the class width was reduced?
5. How would increasing the sample size affect the shape of the histogram?

### Tip:
When interpreting histograms, focus on the shape and spread of the data. This can give insight into patterns, such as skewness, central tendencies, and outliers.

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.

This problem involves analyzing a histogram of employee salaries. Learn how to determine the number of classes, estimate the greatest and least frequencies, calculate the class width, and describe patterns in the data. This is suitable for students in Grades 9-12.

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