Question
The youngest person in a company is 29. The oldest is 69. a. What is the range? b. Is the range a good measure of spread for the ages in the company? Why or why not? a. The range is
Ask by Cervantes Tyler. in the United States
Feb 03,2025
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Answer
a. The range is 40 years.
b. The range isn't the best measure of spread because it only considers the youngest and oldest ages, ignoring how the other ages are distributed.
Solution
a. **The range is 40 years.**
*Calculation:*
Range = Oldest age - Youngest age
Range = 69 years - 29 years
Range = 40 years
b. **The range is not the best measure of spread for the ages in the company.**
*Explanation:*
While the range provides a quick snapshot of the spread by showing the difference between the youngest and oldest ages, it has several limitations:
1. **Sensitivity to Outliers:** The range only considers the two extreme values. If there's an unusually young or old employee that isn't representative of the overall age distribution, the range can be misleading.
2. **Lack of Detail:** It doesn't provide any information about how the other employees' ages are distributed between the youngest and oldest. For instance, the majority of employees might be clustered around the average age, but the range wouldn't reflect this concentration.
3. **Doesn't Reflect Variability:** Other measures like the interquartile range or standard deviation offer a better understanding of the data's variability by considering more data points.
Therefore, while the range offers a basic idea of the spread, using additional statistical measures would provide a more comprehensive view of the age distribution within the company.
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The range is 40 years, calculated by subtracting the youngest age (29) from the oldest age (69). So, 69 - 29 = 40. Now, while the range gives you a quick idea of the age spread, it can be a little misleading. Imagine a company where most employees are clustered around 30 years old, but there are a couple of outliers at 60 and 69. The range of 40 years sounds dramatic even if the majority are close in age. This is why considering other measures like the interquartile range or standard deviation can paint a clearer picture of the actual spread.