Measure of Central Tendency

A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data

Mean (Average)

MeanIt is the average of a set of numbers or observations. To calculate it add up all the observations and then divide by number (count) of observations.
•Population Mean (µ) = Sum of observations (x) for entire population / N = (∑1_(i=1)^Nxi)/N
•Sample Mean (x̅)  =  Sum of observations (x) for sample population / n = (∑1_(i=1)^nxi)/n
•Weighted mean xw = (∑1_(i=1)^N▒〖wi. xi〗)/Σwi
•Meaningful for interval and ratio data
•Affected by unusually large or small observations (outliers).
•Sum of deviation of each value from the mean is Zero

Mode (Most Frequent)

Mode•Observation that occurs most frequently
•Mode is normally used for categorical data where we wish to know which is the most common category
•For grouped data, it is the midpoint of the cell with largest frequency
•Meaningful for interval, ratio, ordinal and nominal data
•One of the problems with the mode is that it is not unique. This happens mostly with continuous data and hence mode is very rarely used with continuous data
•Mode also does not provide with a good measure of central tendency when the most common mark is far away from the rest of the data in the data set

Median (Middle Value)

Median•Middle value when data is ordered
•If odd number of data points, then it is the mid data point (n +1)/2
•If even number of data points, then it is the average of mid two values (n/2) & (n/2)+1
•Meaningful for interval, ratio and ordinal data
•It is the preferred method to measure central tendency in case data is skewed or contains outliers as it is NOT affected by outliers (unusually large or small observations) and skewed data