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The range is the simplest measure of dispersion and it represents the difference between the highest and lowest values in a data set. To calculate the range, you follow these steps:
1. Identify the maximum value in your data set.
2. Identify the minimum value in your data set.
3. Subtract the minimum value from the maximum value.
For example, if your data set is {3, 7, 8, 2, 10}, the maximum value is 10 and the minimum value is 2. The range is 10 - 2 = 8.
The range gives a quick idea of how spread out the data is, but it doesn't provide information about the distribution of the values between the extremes.

Variance measures how much the values in a data set deviate from the mean. It provides a sense of the overall spread and is calculated as follows:
1. Find the mean (average) of the data set.
2. Subtract the mean from each value to find the deviation for each value.
3. Square each deviation.
4. Calculate the average of these squared deviations.
For instance, for the data set {4, 8, 6, 5, 3}, the mean is 5.2. The deviations are {-1.2, 2.8, 0.8, -0.2, -2.2}. Squaring these deviations gives {1.44, 7.84, 0.64, 0.04, 4.84}. The variance is the mean of these squared deviations: \( \frac{1.44+7.84+0.64+0.04+4.84}{5} = 2.96\).
While variance provides a good measure of spread, because it squares the deviations, the unit of variance is the square of the unit of the original data.

Standard deviation is a commonly used measure of dispersion that also measures the average distance of the data points from the mean. However, unlike variance, it is in the same unit as the original data, making it easier to interpret. Here's how you calculate it:
1. Calculate the variance of the data set.
2. Take the square root of the variance.
For example, using the variance from the previous example (2.96), the standard deviation is \( \sqrt{2.96} = 1.72 \).
Standard deviation is very useful in statistics because it tells you how spread out the values are in your data set. The smaller the standard deviation, the closer the data points are to the mean. A larger standard deviation indicates that the data points are spread out over a larger range of values.