Descriptive statistics provide information about the central location (central tendency), dispersion (variability or spread), and shape of the distribution.
Useful when the values are rates and ratios.
Useful when the values are percentages.
Also known as the coefficient of variation or relative standard deviation.
Skewness can be positive or negative. Negative skew indicates that the tail on the left side of the distribution is longer or fatter than the right side. Positive skew indicates the converse, the tail on the right side is longer or fatter than the left side. A value of zero indicates the tails on both sides balance; this is the case for symmetric distributions, but also for asymmetric distributions where a short fat tail balances out a long thin tail.
Positive excess kurtosis (called leptokurtic) indicates the distribution has fatter tails than a normal distribution. Negative excess kurtosis (called platykurtic) indicates the distribution has thinner tails than a normal distribution.
For normally distributed data, the mean and standard deviation provide the best measures of central location and dispersion.
For data with a non-normal or highly-skewed distribution, or data with extreme values, the median and the first and third quartiles provide better measures of central location and dispersion. When the distribution of the data is symmetric, the inter-quartile range (IQR) is a useful measure of dispersion. Quantiles further describe the distribution of the data, providing an interval containing a specified proportion (for example, 95%) of the data or by breaking the data into intervals each containing a proportion of the data (for example, deciles each containing 10% of the data).
