"An average value is a single value within the range of the data that is used to represent all of the values in the series. Since an average is somewhere within the range of the data, it is sometimes called a measure of central value." (Frederick E Croxton & Dudley J Cowden, "Practical Business Statistics", 1937
"A good estimator will be unbiased and will converge more and more closely (in the long run) on the true value as the sample size increases. Such estimators are known as consistent. But consistency is not all we can ask of an estimator. In estimating the central tendency of a distribution, we are not confined to using the arithmetic mean; we might just as well use the median. Given a choice of possible estimators, all consistent in the sense just defined, we can see whether there is anything which recommends the choice of one rather than another. The thing which at once suggests itself is the sampling variance of the different estimators, since an estimator with a small sampling variance will be less likely to differ from the true value by a large amount than an estimator whose sampling variance is large." (Michael J Moroney, "Facts from Figures", 1951)
"The mode would form a very poor basis for any further calculations of an arithmetical nature, for it has deliberately excluded arithmetical precision in the interests of presenting a typical result. The arithmetic average, on the other hand, excellent as it is for numerical purposes, has sacrificed its desire to be typical in favour of numerical accuracy. In such a case it is often desirable to quote both measures of central tendency.(Michael J Moroney,Facts from Figures", 1951)
"An average is sometimes called a 'measure of central tendency' because individual values of the variable usually cluster around it. Averages are useful, however, for certain types of data in which there is little or no central tendency." (William A Spirr & Charles P Bonini,Statistical Analysis for Business Decisions" 3rd Ed., 1967)
"Central tendency is the formal expression for the notion of where data is centered, best understood by most readers as 'average'. There is no one way of measuring where data are centered, and different measures provide different insights." (Charles Livingston & Paul Voakes,Working with Numbers and Statistics: A handbook for journalists", 2005)
"Distributional shape is an important attribute of data, regardless of whether scores are analyzed descriptively or inferentially. Because the degree of skewness can be summarized by means of a single number, and because computers have no difficul ty providing such measures (or estimates) of skewness, those who prepare research reports should include a numerical index of skewness every time they provide measures of central tendency and variability." (Schuyler W Huck, "Statistical Misconceptions", 2008)
"It is best to think of the various kinds of central tendency indices as falling into three categories based on the computational procedures one uses to summarize the data. One category deals with means, with techniques put into this category if scores are added together and then divided by the number of scores that are summed. The second category involves different kinds of medians, with various techniques grouped here if the goal is to find some sort of midpoint. The third category contains different kinds of modes, with these techniques focused on the frequency with which scores appear in the data." (Schuyler W Huck, "Statistical Misconceptions", 2008)
"Various measures of central tendency have been invented because the proper notion of the 'average' score can vary from study to study. Depending on the kind of data collected, the degree of skewness in the data, and the possible existence of outliers, it may be that the most appropriate measure of central tendency is found by doing something other than (1) dividing the sum of the scores by the number of scores (to get the mean), (2) calculating the midpoint in the distribution (to get the median), or (3) determining the most frequently observed score (to get the mode)." (Schuyler W Huck, "Statistical Misconceptions", 2008)
"Statistical analysis seeks to develop concise summary figures which describe a large body of quantitative data. One of the most widely used set of summary figures is known as measures of location, which are often referred to as averages, measures of central tendency or central location. The purpose for computing an average value for a set of observations is to obtain a single value which is representative of all the items and which the mind can grasp simply and quickly. The single value is the point or location around which the individual items cluster." (Lawrence J Kaplan)
