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The 68-95-99.7 rule is an easy way to understand how data is spread in a normal distribution. Whenever you're dealing with normally distributed data, this rule gives you a quick insight into where most of your data values lie. This rule is sometimes called the empirical rule and is based on the properties of the normal distribution:

• 68% of the data falls within one standard deviation from the mean.
• 95% of the data falls within two standard deviations from the mean.
• 99.7% of the data falls within three standard deviations from the mean.

This means if you know the mean and standard deviation of a data set, you can easily find the range where most of the data falls.
In the exercise, you use the 68-95-99.7 rule to find the limits within which about 95% of the individuals' daily active minutes lie. For mildly obese people, with a mean of 373 minutes and a standard deviation of 67, you calculate this by adding and subtracting two times the standard deviation from the mean. This approach is repeated for lean people, resulting in their specific range of active minutes. By understanding this simple rule, you can apply it in various scenarios involving normally distributed data.

The standard deviation of a data set is a key measure that shows how much the data values deviate from the mean. In simpler terms, it tells you how spread out the numbers are. A small standard deviation means the data points are close to the mean, while a large standard deviation indicates a wider spread around the mean.
Calculating standard deviation might look daunting, but its concept is straightforward:

• Find the mean (average) of your data set.
• Subtract the mean from each data point to find the deviation of each one.
• Square each deviation to remove negative values.
• Find the average of these squared deviations.
• Take the square root of that average to obtain the standard deviation.

In the exercise, the standard deviation helps determine the spread of daily active minutes for different groups. For mildly obese individuals, the standard deviation is 67, showing the variability in their activity levels. Similarly, for lean individuals, a standard deviation of 107 implies a broader range of activity minutes. Understanding standard deviation helps predict how typical or atypical a certain data point might be.

The mean is one of the most basic concepts in statistics, commonly referred to as the average. To calculate the mean, you add up all the numbers and divide by the number of data points. It represents the center of a data set, providing a simple summary of the overall trend or "central tendency."
Here's how you generally find the mean:

• Add all the data points together.
• Divide the total by the number of data points.

In the normal distribution described in the exercise, the mean gives you an idea of the average amount of time people in each group spend being active. For instance, mildly obese individuals have a mean activity level of 373 minutes per day, while lean individuals have a mean of 526 minutes. The mean's role in the 68-95-99.7 rule is crucial, as it serves as a reference point for calculating the standard deviations needed to determine where most data points lie.