sample: re-write of statistics textbook

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Introduction to Statistical Methods and Data Analysis

Ott,  2nd ed.

Duxbury Press (1984)

pg. 22-on

      Numerical descriptive measures are commonly used to convey a mental image of pictures, objects, and other phenomena. There are two main reasons for this: first, graphical descriptive measures are inappropriate for statistical inference, since it is difficult to describe the similarity of a sample frequency histogram and the corresponding population frequency histogram. The second reason for using numerical descriptive measures is one of expediency-we never seem to carry the appropriate graphs or histograms with us, and so must resort to our powers of verbal communication to convey the appropriate picture. We seek several numbers, called numerical descriptive measures, that will create a mental picture of the frequency distribution for a set of measurements. 

     The two most common numerical descriptive measures are measures of central tendency and measures of variability. That is, we seek to describe the center of the distribution of measurements and also how the measurements vary about the center of the distribution. We will draw a distinction between numerical descriptive measures for a population, called parameters, and numerical descriptive measures for a sample,called statistics. In problems requiring statistical inference, we will not be able to calculate values for various parameters, but we will be able to compute corresponding statistics from the sample and use these quantities to estimate the corresponding population parameters.

[Following sections detail specific measurements

 mode

 median

 mean

 vs

 range

 nth percentile

 interquartile range

 deviation

      As you will recall from previous sections, we draw a clear distinction between populations and samples, populations being a group of things we are interested in and samples being manageable subsets of that group.

      At this point, we can now introduce the concept of numerical descriptive measures, which are numbers used to convey information, as opposed to graphical measures, which are pictures used to convey information.  (Examples of graphical measures would be things like graphs, charts, etc.)

      With the above concepts, we can now draw a distinction between numerical descriptive measures for populations, which are called parameters, and numerical descriptive measures for samples, these being called statistics.  The overall idea behind these distinctions is employed in problems requiring statistical inference, or in other words, in the process of making decisions on the basis of statistics.  In these statistical inferences, we will not be able to calculate values for various parameters of the population, but we will be able to compute statistics from the sample and use these quantities to estimate the corresponding population parameters.  And this is the main reason for making a thorough study of statistics and statistical methods:  Use numerical-based methods on samples, and by doing so, make good estimates about populations.  

      There are at least two good reasons to favor the use of numerical descriptive measures in this process:  First, its relatively difficult to make precise decisions based on pictures; for example, we can tell when one bar on a bar graph is bigger than another, but it is very hard to tell exactly how much bigger it is just based on the picture.  Second, it is a lot easier and faster to report exact numbers than it is to draw exact pictures; and pictures take a up a lot more space, so numbers have a lot of convenience on their side.

     Now then, the two most common numerical descriptive measures are:

(a)  measures of central tendency

      These describe the center of the distribution of measurements; for example, the median (the middle measurement of a list) or the mean (the average)

(b)  measures of variability

      These describe how the measurements vary about the center of the distribution; for example, what is called the deviation.

      At this point, we can review each of these measures in detail.