To solve this problem using the information provided about the histogram and data:

Assumptions:

1. The histogram represents Employee Salaries with class midpoints labeled as:
   • $34.5, 44.5, 54.5, 64.5, 74.5, 84.5, 94.5$.
2. Frequencies for the respective midpoints are given:
   • $0, 100, 200, 300, 200, 100, 0$.

Let’s solve the problem step-by-step:

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(a) Determine the number of classes.

The number of classes is the total number of distinct intervals represented in the histogram. From the midpoints provided: $34.5, 44.5, 54.5, 64.5, 74.5, 84.5, 94.5$ The number of midpoints is 7, so there are 7 classes.

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(b) Estimate the greatest and least frequencies.

From the provided frequencies:

• The least frequency is $0$ (occurring at $34.5$ and $94.5$).
• The greatest frequency is $300$ (occurring at $64.5$).

Thus: $\text{Least frequency: } 0, \quad \text{Greatest frequency: } 300$

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(c) Determine the class width.

To calculate class width, we take the difference between consecutive class midpoints. From the midpoints $34.5, 44.5, 54.5, \ldots$: $\text{Class width} = 44.5 - 34.5 = 10$

The class width is 10.

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(d) Describe any patterns with the data.

Analyzing the frequency distribution:

1. The frequencies follow a symmetrical distribution:
   • The frequencies increase from $0$ to $300$ and then decrease symmetrically back to $0$.
2. The data represents a bell-shaped curve, suggesting that the salaries are normally distributed around a central point ($64.5$ midpoint).

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Final Summary:

• (a) Number of classes: $7$
• (b) Greatest frequency: $300$, Least frequency: $0$
• (c) Class width: $10$
• (d) Pattern: Symmetrical distribution (bell-shaped).

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Do you want detailed calculations for any part? Let me know!

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Related Questions:

1. How can you verify the class width from histogram boundaries instead of midpoints?
2. What does a symmetrical bell-shaped histogram indicate about a dataset's central tendency?
3. Can you find the range of salaries based on this histogram?
4. How would the frequencies change if the distribution were skewed left or right?
5. How could the mean salary be estimated from the histogram?

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Tip:

When analyzing histograms, always check if the data distribution is symmetrical or skewed—it reveals key insights about the dataset.