Standard Deviation, Mean and Median

Standard Deviation

Standard Deviation measures the amount of variation or dispersion from the average in a set of values. A low standard deviation means that the values are close to the mean, while a high standard deviation means the values are spread out over a larger range.
The formula for calculating standard deviation is quite complex. It involves subtracting the mean from every value (giving the deviations), squaring those values (giving the squared deviations), calculating the average of those squared deviations (this gives the variance), and then finding the square root of the variance (this gives the standard deviation).
You can use the empirical rule in a normal distribution (which is a bell-shaped curve) to determine the percentage of data within certain number of standard deviations from the mean. Approximately 68% of data falls within the first standard deviation, 95% within the first two standard deviations, and 99.7% within the first three.

The mean, or average, is calculated by adding up all the values, and then dividing by the number of values.
The mean can be heavily influenced by outliers (unusually high or low values in the data set), which can sometimes make it a less reliable measure of centre.
The mean is the only measure of central tendency where the total of all the values is distributed evenly among them.

The median is the middle value when all values are listed in ascending order.
If the data set has an even number of observations, the median is the average of the two middle numbers.
Unlike the mean, the median is not affected by outliers. If the distribution of data is skewed (not symmetrical), the median is often a better choice for the best measure of central tendency.
Finding the median divides a data set into two equal halves. The number of data points above the median is equal to the number below.