Basic Statistics Summary for Normal Distribution

For more general applications, you may want to know a bit more about statistical metrics. As a brief summary, the basic statistics include mean, standard deviation, quartiles, standard error, and confidence intervals. Let us explain the physical 

Mean is the most important metric, which describes the peak location of the distribution. It is calculated the same as the arithmetic average expressed in equation (21.2). 

Median is the middle value of the Monte Carlo simulation data when they are sorted from low to high. In other words, 50% of the data is less than the median. If there is an even number of data points, then the median is the average of the middle two points. In spreadsheet, the sample mean = Average (array) and the sample median = Median (array). 

Extreme values can have a large impact on the mean, but the median only depends upon the middle point(s). This property makes the median useful for describing the center of skewed distributions. In concept, the mean and median are different. If the distribution is symmetric (like the Normal distribution), then the values of mean and median are identical. 

This is the second most important metric as it is the measure of dispersion deviation from mean in root squared form (see equation (21.3)). In other words, the standard deviation describes the spread of the data. 

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