24 May 2017

Measures of Location–Mean and Median

Measures of location are used in order to determine where the data distribution is concentrated. The most usual measures of location are Mean and Median


The mean of a set of numerical observations is just the familiar arithmetic average. The sum of the observations divided by the number of observations gives you Arithmetic Mean. It is helpful to have concise notation for the variable on which observations were made.



x = the variable for which we have sample data

n = the number of observations in the sample (the sample size)

x1 = the first observation in the sample

x2 = the second observation in the sample

xn = the nth (last) observation in the sample

The Greek letter Ʃ is traditionally used in mathematics to denote summation. It denotes the sum of all the x values in the data set.


Like a median strip of a highway divides the highway in half, the median of a numerical data set does the same thing for a data set. Once the data values have been listed in order from smallest to largest, the median is the middle value in the list, and it divides the list into two equal parts. Depending on whether the sample size n is even or odd, the process of determining the median is slightly different. When n is an odd number (say, 7), the sample median is the single middle value. But when n is even (say, 8), there are two middle values in the ordered list, and we average these two middle values to obtain the sample median.


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