(c) Eliminate the high salary of 280 thousand dollars. Make a new histogram using the class boundaries 53.5, 62.5, 71.5, 80.5, 89.5, 98.5.

Consider the following histograms and their corresponding data:

1. Histogram 1:
- Horizontal axis: "Salaries" (53.5 to 98.5)
- Vertical axis: "Frequency" (0 to 15)
- Data:
- 53.5 to 62.5: 6
- 62.5 to 71.5: 6
- 71.5 to 80.5: 5
- 80.5 to 89.5: 11
- 89.5 to 98.5: 7

2. Histogram 2:
- Horizontal axis: "Salaries" (53.5 to 98.5)
- Vertical axis: "Frequency" (0 to 15)
- Data:
- 53.5 to 62.5: 7
- 62.5 to 71.5: 11
- 71.5 to 80.5: 5
- 80.5 to 89.5: 6
- 89.5 to 98.5: 6

3. Histogram 3:
- Horizontal axis: "Salaries" (53.5 to 98.5)
- Vertical axis: "Frequency" (0 to 15)
- Data:
- 53.5 to 62.5: 5
- 62.5 to 71.5: 6
- 71.5 to 80.5: 6
- 80.5 to 89.5: 7
- 89.5 to 98.5: 11

4. Histogram 4:
- Horizontal axis: "Salaries" (53.5 to 98.5)
- Vertical axis: "Frequency" (0 to 15)
- Data:
- 53.5 to 62.5: 11
- 62.5 to 71.5: 7
- 71.5 to 80.5: 6
- 80.5 to 89.5: 6
- 89.5 to 98.5: 5

Question: Does this histogram reflect the salary distribution of most of the employees better than the histogram in part (a)?

A. Yes
B. No

Yes, this histogram better reflects the salary distribution of most employees. By removing the high salary of 280,000 dollars, the dataset becomes more representative of typical salaries. The adjusted histogram provides a clearer view of salary trends without the distortion caused by an extreme outlier.

Step-by-step explanation:

Step 1: Identify the Outlier

A salary of 280,000 dollars is significantly higher than the other values in the dataset.

This single extreme value can skew the histogram, making it misleading.

Most employees likely have salaries much lower than this.

Step 2: Remove the Outlier

By eliminating 280,000 dollars, we focus on the salaries that better represent the majority of employees.

This ensures a more balanced and meaningful visualization of the data.

Step 3: Create a New Histogram with Given Class Boundaries

The histogram has class boundaries: 53.5, 62.5, 71.5, 80.5, 89.5, 98.5.

Each interval has a frequency (number of employees in that range).

New Histogram Data: | Salary Range (in $1000s) | Frequency | |--------------------------|-----------| | 53.5 - 62.5 | 11 | | 62.5 - 71.5 | 7 | | 71.5 - 80.5 | 6 | | 80.5 - 89.5 | 6 | | 89.5 - 98.5 | 5 |

Step 4: Compare with the Original Histogram

The original histogram included the outlier, which may have shifted the data, affecting class distributions.

The new histogram removes this distortion, ensuring the salaries are evenly distributed across intervals.

It provides a more realistic representation of most employees’ salaries.

Step 5: Answer the Question

Does this new histogram reflect the salary distribution better?

Yes. It focuses on the most common salary ranges without being affected by an extreme value.