Answer :
The 68-95-99.7 rule guides the understanding of normal distribution, indicating that within one, two, and three standard deviations from the mean, approximately 68%, 95%, and 99.7% of data points lie, respectively.
The 68-95-99.7 rule, often referred to as the empirical rule, provides a valuable guideline for understanding the distribution of data in a normal distribution. According to this rule, which applies specifically to normal distributions:
Approximately 68% of observed data points fall within one standard deviation of the mean.
Roughly 95% of data points fall within two standard deviations of the mean.
Almost 99.7% of data points fall within three standard deviations of the mean.
To illustrate, consider a normal distribution graph. Within one standard deviation from the mean, encompassing the central and most frequent values, about 68% of the data lies. As we extend to two standard deviations, we capture a broader range, covering 95% of the data. Going further to three standard deviations, an even larger portion, approximately 99.7% of the data, is included.
Applying this rule to a specific scenario, if we shade the region within one standard deviation of the mean on the graph, it represents the central 68% of the population, emphasizing the concentration of data around the mean.
In summary, the 68-95-99.7 rule provides a statistical framework to interpret the spread of data in a normal distribution, emphasizing the significance of standard deviations from the mean.
