Critical Thinking: The Following Data Represents Salaries

Critical Thinkingthe Following Data Represent Salaries In Thousands O

Critical Thinking The following data represent salaries, in thousands of dollars, for employees of a small company. Make a histogram using the class boundaries 23.5, 69.5, 115.5, 161.5, 207.5, 253.5. Then, examine the last data value to determine if it appears to be an outlier and consider whether it might be the owner's salary. Next, eliminate the high salary of 250 thousand dollars and create a new histogram using the class boundaries 23.5, 32.5, 41.5, 50.5, 59.5, 68.5. Finally, assess whether this new histogram better reflects the salary distribution of most employees than the first histogram.

Paper For Above instruction

The analysis of salary data within organizations can unveil critical insights into income distribution, employee equity, and potential outliers that may skew overall perceptions. In this context, creating histograms based on specific class boundaries offers a visual approach to comprehend the salary spread among employees. The initial task involves constructing a histogram with class boundaries set at 23.5, 69.5, 115.5, 161.5, 207.5, and 253.5. Such boundaries segment the data into ranges that typically capture low to high salaries, enabling an understanding of the overall distribution pattern. By plotting salary frequencies within these classes, one can identify clusters, gaps, or outliers that indicate unusual salary levels or concentration points.

In an application of this method, the last salary entry, which is significantly higher than the others, warrants particular scrutiny. If that data point appears isolated, it may be an outlier—a value that deviates markedly from other observations. Outliers can arise from extraordinary circumstances such as a company founder’s or owner’s salary, which might be substantially higher than regular employee earnings. Recognizing such a deviation is vital because outliers can distort statistical measures like mean and variance, affecting interpretations and decisions.

To mitigate the influence of the outlier, the subsequent step involves removing the salary of 250 thousand dollars from the dataset. The revised salary data is then used to construct a new histogram with narrower class boundaries, ranging from 23.5 to 68.5 in increments of 9. That is, the class intervals are 23.5–32.5, 32.5–41.5, 41.5–50.5, 50.5–59.5, and 59.5–68.5. This finer segmentation enables a more detailed view of the salary distribution for the majority of employees, likely revealing the central tendencies and spread more clearly without the distortion of an extreme outlier.

Comparing the two histograms—before and after removing the high salary—provides insights into data distribution. The first histogram might show a right-skewed distribution with a long tail due to the outlier, potentially overstating the typical employee salary. Conversely, the second histogram, with adjusted boundaries and the removal of the outlier, is expected to better reflect the salaries of most employees, highlighting the core salary range and showing a more balanced distribution. Such analysis supports more accurate organizational assessments, salary equity evaluations, and informed decision-making regarding pay structures.

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