Calculate the Standard Deviation of Sample Ages

Five students in a college were selected at random and their ages were found to be 18, 21, 19, 20, and 26. Calculate the standard deviation of the ages in the sample.

This problem involves calculating the standard deviation of a sample, which is a measure of how spread out the ages of the students are from the mean age. In statistics, the standard deviation is a crucial concept as it helps us understand variability in data. When we calculate the standard deviation for a sample, we divide by n-1 rather than n to account for the bias in sampling small data sets - this is known as Bessel's correction. This problem highlights an essential aspect of descriptive statistics, providing a hands-on experience with variability measurement and reinforcing the importance of using unbiased estimators for statistical parameters.

The task also underlines how data analysis can provide insights. A smaller standard deviation indicates that the data points (ages, in this case) tend to be closer to the mean, suggesting that the ages of the students are relatively similar. Conversely, a larger standard deviation would imply greater variability in the data. As a student learning about descriptive statistics, grasping how to calculate and interpret the standard deviation in a sample is pivotal. This comprehension enables you to apply statistical concepts to real-world scenarios and enhances your analytical skills.