How do you calculate the variance in a data set with 'n' values?

To calculate the variance in a data set with 'n' values, the correct approach involves first determining the mean of the data set. After obtaining the mean, the next step is to calculate the squared differences from the mean for each data point. This requires subtracting the mean from each data value, squaring that result, and then summing all those squared differences. Finally, you divide this total by 'n', the number of values in the data set.

This process captures the dispersion of the data points relative to the mean, allowing for a comprehensive assessment of variability within the dataset. The use of 'n' in the division step reflects that you are calculating the population variance, which represents the average of the squared differences for the entire population of data points.

Other methods mentioned, such as summing the data and dividing by 'n', would yield the mean, not the variance; multiplying the mean by 'n' would give you the total of the data points; and finding the maximum and minimum values would not provide insight into overall variability, as it only considers the extremes. Therefore, summing the squared differences and dividing by 'n' is the appropriate method to calculate variance accurately.