# Descriptive Statistics

A data can have one or more than one mode.If there is only one number that appears maximum number of times, the data has one mode, and is called Uni-modal.If there are two numbers that appear maximum number of times, the data has two modes, and is called Bi-modal.If there are more than two numbers that appear maximum number of times, the data has more than two modes, and is called Multi-modal.Example to compute the Measures of Central TendencyConsider the following data points.17, 16, 21, 18, 15, 17, 21, 19, 11, 23Mean — Mean is calculated asMedian — To calculate Median, lets arrange the data in ascending order.11, 15, 16, 17, 17, 18, 19, 21, 21, 23Since the number of observations is even (10), median is given by the average of the two middle observations (5th and 6th here).Mode — Mode is given by the number that occurs maximum number of times..Here, 17 and 21 both occur twice..Hence, this is a Bimodal data and the modes are 17 and 21.Note-Since Median and Mode does not take all the data points for calculations, these are robust to outliers, i.e..these are not effected by outliers.At the same time, Mean shifts towards the outlier as it considers all the data points..This means if the outlier is big, mean overestimates the data and if it is small, the data is underestimated.If the distribution is symmetrical, Mean = Median = Mode..Normal distribution is an example.Measures of Dispersion (or Variability)Measures of Dispersion describes the spread of the data around the central value (or the Measures of Central Tendency)Absolute Deviation from Mean — The Absolute Deviation from Mean, also called Mean Absolute Deviation (MAD), describe the variation in the data set, in sense that it tells the average absolute distance of each data point in the set..It is calculated as2..Variance — Variance measures how far are data points spread out from the mean..A high variance indicates that data points are spread widely and a small variance indicates that the data points are closer to the mean of the data set..It is calculated as3..Standard Deviation — The square root of Variance is called the Standard Deviation..It is calculated as4.. More details