Let's analyze the histogram and solve the given questions step by step:

(a) Determine the number of classes.

• Classes represent the number of intervals on the x-axis of the histogram.
• From the histogram, we can see the x-axis is divided into 7 intervals:
  • 34.5–44.5
  • 44.5–54.5
  • 54.5–64.5
  • 64.5–74.5
  • 74.5–84.5
  • 84.5–94.5

So, number of classes = 7.

(b) Estimate the greatest and least frequencies.

• Greatest frequency: The tallest bar is around the class 54.5–64.5, and it appears to have a frequency of approximately 300.
• Least frequency: The shortest bar is in the class 34.5–44.5, which has a frequency close to 50.

Thus:

• Greatest frequency ≈ 300
• Least frequency ≈ 50

(c) Determine the class width.

• The class width is the difference between the lower and upper boundaries of a class.
• For instance, the width of the class 34.5–44.5 is $44.5 - 34.5 = 10$.

So, the class width = 10.

(d) Describe any patterns with the data.

• Most of the employees seem to have salaries in the range of 54.5k to 64.5k dollars, which has the highest frequency.
• The data shows a skew to the right, meaning that while most employees earn lower salaries, there are a few higher salaries in the range 84.5k–94.5k dollars.
• There is a gradual decrease in frequency as salary increases beyond the most common range.

Would you like further details on any part of this explanation?

Relative questions:

1. How would the interpretation of the data change if the class width were different?
2. Can you calculate the total number of employees using the histogram?
3. What can be inferred about salary distribution if we know the median salary class?
4. How would you adjust the histogram to better represent data variation at the high end of salaries?
5. Can you identify any potential outliers in this data set based on the histogram?

Tip:

When analyzing histograms, always check both the distribution shape (e.g., skewness, peaks) and the spread of the data, as these can reveal important trends and patterns.