Summarizing Distributions using Statistics

Summary Statistics are used to summarize information regarding a sample.

Important tools in Summary Statistics are

1. Mean
2. Variance
3. Effect Size (https://en.wikipedia. org/wiki/Effect_size)

• A histogram is a complete description of the distribution of a sample, by a histogram a complete reconstruction of the values in a sample can be reconstructed. 

Summarizing a distribution is important and descriptive statistics is used to provide a summary of a sample.

Some important characteristics are 

• Central Tendency: Are the values around a central point,  mean, mode or median. 
• Modes: Is there more than one cluster. ( A modal value, is calculated by counting the number of occurrence of a value.)
• Spread of Data: How much variability is in the data. The variability in the data can be calculated by range, quartiles, variance, absolute deviation and standard deviation.
• Tails: How quickly do the probabilities drop off as we move away from the modes ?
• Outliers: Extreme Values away from the modes, sometimes the result of Errors but other times the result of  unusual data.