https://file.aiquickdraw.com/mathbot/file/17274605970935lxeaqb1.jpg

Let's go through the parts of the question based on the histogram provided in the image.

### (a) Determine the number of classes.
The number of classes refers to the number of intervals or bars on the histogram. Based on the histogram in the image, I can see there are **6 classes**.

### (b) Estimate the greatest and least frequencies.
- The tallest bar has a height of around **300**, which would be the greatest frequency.
- The shortest bar has a height of **50**, which is the least frequency.

### (c) Determine the class width.
The class width is the difference between the lower boundaries of two consecutive classes. Looking at the salary ranges:
- The first class starts at 34.5 and the next class starts at 44.5, so the class width is:
  \[
  \text{Class width} = 44.5 - 34.5 = 10 \, \text{(thousand dollars)}
  \]

### (d) Describe any patterns with the data.
The data shows a peak around the middle classes, with a frequency of around 300 employees, and tails off at the extremes. This pattern suggests that most employees' salaries cluster around the middle salary ranges, with fewer employees earning salaries at the high and low extremes.

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Would you like further details on any part?  
Here are some related questions to consider:

1. What is the general definition of a frequency histogram?
2. How do you calculate class intervals if the data is not given in a histogram?
3. What are the common patterns or shapes you can expect from a histogram?
4. How do you calculate relative frequency, and would it affect the interpretation of the histogram?
5. What might skewness in the data tell us about salary distribution?

**Tip**: When working with histograms, always verify the scale of the axes to ensure correct interpretation of frequencies and values.

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 by determining the number of classes, estimating greatest and least frequencies, calculating class width, and identifying patterns in the data. This example uses employee salaries as a real-world dataset.

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