The U.S. Supreme Court Chief Justice data was used to create the following output in an Excel spreadsheet. Choose statement that best summarizes the variability of the dataset. Standard Error 1.86 Standard Deviation 5.59 Sample Variance 31.27 Range 18 Minimum 50 Maximum 68 Sum 553 Count 9 The age of most of the U.S. Supreme Court Chief Justice’s since 1900 are within 5.6 years of the mean age. The ages of most of the U.S. Supreme Court Chief Justices are between 50 and 68 years The age of most of the U.S. Supreme Court Chief Justice’s since 1900 are within 31.3 years of the mean age.
The Correct Answer and Explanation is:
The correct statement that best summarizes the variability of the dataset is:
“The ages of most of the U.S. Supreme Court Chief Justices are between 50 and 68 years.”
Explanation:
The provided dataset gives several statistical measures about the ages of U.S. Supreme Court Chief Justices since 1900. To understand the variability of the data, let’s break down the key metrics:
- Standard Error (1.86):
This measures the precision of the sample mean. It tells us how much the sample mean (average age) is likely to vary from the true population mean. A standard error of 1.86 is relatively small, meaning the mean age is quite reliable for this sample. - Standard Deviation (5.59):
This tells us how spread out the ages are from the mean. In this case, most ages are within 5.59 years of the mean. It indicates moderate variability in the ages of Chief Justices. - Sample Variance (31.27):
This is the square of the standard deviation and tells us how much the data varies. A variance of 31.27 means the squared deviations of the ages from the mean are, on average, 31.27 years squared. - Range (18):
This is the difference between the maximum and minimum ages, which are 68 and 50, respectively. The range of 18 years suggests the ages are confined to a relatively narrow interval. - Minimum (50) and Maximum (68):
These values directly indicate that the ages are between 50 and 68 years.
Conclusion:
Given that the maximum age is 68 and the minimum is 50, the second statement “The ages of most of the U.S. Supreme Court Chief Justices are between 50 and 68 years” is the most accurate. It captures the practical range of the ages, showing how most data points are confined within this range.
The first and third statements mention the standard deviation and variance, but they don’t fully encompass the overall variability as effectively as the range. The range directly provides the minimum and maximum ages, which are easier to understand and summarize the variability.
