Final answer:
A real-world example of standard deviation is classroom test scores, where the standard deviation shows how much the scores vary from the average. Using the empirical rule, we can estimate that approximately 95% of data in a normal distribution fall within two standard deviations of the mean. Understanding standard deviation helps assess data dispersion.
Step-by-step explanation:
A real-world example of standard deviation is test scores in a classroom. Imagine the final exam scores in a statistics class that were normally distributed with a mean of 63 and a standard deviation of five. This standard deviation indicates that most of the students scored within a range of five points above or below the mean score, showing how much the scores varied from the average.
The empirical rule suggests that for a normal distribution, about 95% of the data will be within two standard deviations from the mean. For instance, using our example of exam scores, we can predict that roughly 95% of the scores lie between 53 (63 - 2*5) and 73 (63 + 2*5). This demonstrates the practical importance of understanding standard deviation in evaluating the spread or dispersion of a data set.
It is advisable to use a calculator or computer software to calculate the standard deviation. However, understanding the concept is crucial. The standard deviation is always positive or zero and gives insight into the spread of data around the mean, indicating whether the data points are closely clustered or widely dispersed.