91Ó°ÊÓ

The range in a set of numbers represents the spread between the smallest and the largest values, giving us an idea of how far apart the numbers are. It's one of the basic measures of dispersion in descriptive statistics.
To calculate the range, you simply identify the maximum and minimum values in your data set and subtract the minimum from the maximum.

• Find the maximum value (the largest number in your set).
• Find the minimum value (the smallest number in your set).
• Subtract the minimum value from the maximum value.

In our example of hours spent partying, the range is calculated as 45 (maximum value) minus 0 (minimum value) which equals 45. This tells us there is a broad variability in how much time students spend partying.

Variance gives us insight into the degree of spread or dispersion in a data set. Unlike the range, which only considers the extreme values, variance takes into account how all the values in the set distribute themselves around the mean.
To compute the variance, follow these steps:

• First, calculate the mean (average) of your data numbers. This is done by adding up all the numbers and dividing by the count of numbers.
• Next, subtract the mean from each number to find the deviation of each number from the mean.
• Square each of these deviations to eliminate any negative values and to emphasize larger deviations.
• Finally, calculate the average of these squared deviations. This result is your variance.

In the aforementioned data, the mean is 8.2, and after calculating the squared deviations and their average, we arrive at a variance of 138.16. This value indicates how much the students' partying hours differ from the average.

The standard deviation is a related concept to variance; however, it provides a more intuitive sense of the spread of a data set because it is in the same units as the original data. By finding the square root of the variance, we bring the measure back to the original scale.
Here is how you calculate the standard deviation:

• First, make sure you have the variance (we calculated this as 138.16).
• Take the square root of the variance to find the standard deviation.

This step converts the variance into a more comprehensible value. In our problem, the square root of the variance (138.16) gives us a standard deviation of approximately 11.75. This means that, on average, the hours spent partying deviates by 11.75 hours from the mean. The lower the standard deviation, the closer the data points tend to be to the mean, suggesting less variability.