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chapter3 - Chapter 3 Numerical Descriptive Techniques...

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Chapter 3 Numerical Descriptive Techniques Descriptive statistics consists not only of graphical summaries, but also numerical methods. Since we have introduced the histogram in the last chapter, the most important graphical summary of data, in this chapter we will discuss basic numerical descriptive statistics, which include measures of central location (notably mean, median, and mode), measures of disper- sion or spread (such as range, standard deviation, variance, coefficient of variation, etc.), and measures of relative standing (such as percentiles and quartiles.) 3.1 Measure of central location The arithmetic mean (or average) is the most important measure of cen- tral location and is calculated by summing the values and dividing by the number of values. X = 1 n n X i =1 X i (3.1) The average or arithmetic mean is unique. Also, it is the only measure of 1
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2 CHAPTER 3. NUMERICAL DESCRIPTIVE TECHNIQUES location where the sum of the deviations of each value from the mean is zero. Interestingly, the histogram balances when supported at the arith- metic average. The median, another measure of centrality, is the midpoint of values in a list after they are ordered, say, from the smallest to the largest. The mode is a less used measure of central location which represents the value of the observation that appears most frequently. The median is not affected by extremely large or small values and is therefore a valuable measure of central location when such extreme values do occur. The mode on the other hand can be interpreted as the “fashion category” and is represented by the highest parts or peaks of a histogram.
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