Statistics have become an integral part of society, and help to shape how we live our lives. Statistics affect everything from how many red cars General Motors makes this year, and whether your favourite scent of soap will be discontinued at the Body Shop, to important questions such as crime rates of particular areas, what political party is expected to win the next election, and if certain schools and libraries can hope to have their funding continued. Masses of raw numbers are quite meaningless and need to be transmitted into graphic displays. To do this, statisticians organize specific kinds of information into forms such as histograms, frequencies, and bar graphs to allow for summarization, assimilation, understanding, and the discernment of meaningful trends.
Libraries provide essential learning resources that strengthen and perpetuate formal and informal education. Valid, reliable, and timely statistics are needed for effective use by policymakers in determining the investment of public resources in library development and operations. Data collection activity that seeks to inform decision making must be sensitive to the changes taking place within the library community and in society overall. Statistics are required to make important policies on the future of our libraries. This research report will concentrate on data collected from the 1994 Ontario Public Library Statistics and what can be discerned from them.
Histograms are not rigidly precise charts, but do provide a picture to look at (0'Sullivan 1995,47), and frequency distributions can be graphically displayed with histograms. As can be seen on page two of the attached appendix, the "population served" numbers have been presented in chart form, permitting additional observations to be made. Of the fifty libraries sampled, forty serve populations less than 20,000, with twenty-three of those, providing library service to groups of less than 10,000. Another nine serve populations between 42,000 and 113,562, with the last one having 320,000 to manage. This statistic is called an outlier and has caused the histogram to become positively skewed.
These figures were provided by the Ontario Public Library Statistics (1994), and have painted a disturbing picture of the public library system, providing a strong argument for closing down some smaller libraries to save money. Studying the demographic situation helps to provide essential information for determining priorities in library service. As budgetary concerns grow, fewer town and city enclaves, and small communities can expect to keep their libraries open without private donations or fund raising to generate money. Some must close, while other high density areas should expect new libraries to be built. Should a single facility be required to service 320,000 people? In part, these statistics could be explained by the prevalent demographic trend of large numbers of people moving from small centers to larger urban areas for employment, with no review of library policy in those locales.
For this population data, it is most appropriate to use the median measure of central tendency because these are quantitative variables, with interval values, and they have at least one outlier that is skewing the results (Rowntree 1991,334). The median can give an accurate picture of central tendency because, unlike the mean, it is not affected by extreme values. Measures of central tendency are used to indicate which value is most representative or central in a distribution, and also include mode and mean. The same central tendency measure is most appropriate for the holdings since that frequency distribution is also skewed, and therefore, cannot use the arithmetic mean.
As for the holdings, the histogram shows that forty-one libraries have book stocks that number 75,000 volumes or less. Eight others have bigger holdings, and one, that has caused the chart to be skewed, has more than 1,000,000 in house. Insight into the collection development policy of the Ontario Public Library System can be gathered from this information. For one, volumes are not spread evenly across the library system. This is obvious from the data, but what does it mean?
Possibly that any small towns have libraries with limited collections, and a few bigger libraries have substantial collections. It is these larger libraries that cause the shape of the histogram to be positively skewed. Still, does this literally mean that people living in larger centers have more books per capita than those living in smaller centers?
This is not necessarily so, and can be clearly seen when a histogram is set up for the average number of volumes per capita. For example, a population of 3073, with 24,440 volumes, has a per capita figure of 7.95; and a library servicing 4986 has stock nearing 37,000, or 7.48 per capita. Not all of the smaller libraries have such large per capita scores, but when one sees a library with 54,000 volumes serving 5400 people (10% per capita) this is more than slightly out of proportion.
It seems to demonstrate that there is no equation drawn up to ensure that the same numbers of people have access to the same numbers of books. This is quite unfair when one considers that the quality of education is directly proportional to how much access there is to information sources. This could be indicative of many things, including: communities that have taxpayers willing to spend more money on education and libraries; powerful families or groups pushing for more library services; corporate sponsorship or endowments; or more likely, inherent problems in the system that have caused mismanagement and unfair advantage for some.
Overall, thirty-two of the libraries/population have per capita figures of three and four, with four hovering around two volumes per capita. With the per capita statistics, there is a wide range of data spread across the intervals, and none that skew the chart positively or negatively. Therefore, the measure of central tendency that is most appropriate here is the mean because the values are qualitative, and are not skewed or bimodal (Rowntree 1991,335). If the data were not truly interval, the distribution non-symmetric, and had outliers, the mean could not be used. The mean is the most commonly used central tendency measure and is calculated in frequency distributions that are symmetrical and unimodal (Rowntree 1991,336). The mean cannot be used when there are extreme values, with outliers pulling it away from the median, distorting the statistics.
The statistics discussed in the preceding sections can be described as quantitative statistics. One of the questions that needs to be answered is how much do the values vary? Or, what is a typical value? These can be answered by using the measures of central tendency. For the population figures, the mean sits at 24446.84, and the median at 11010.5. The mean has been pulled away from the center by the outlier and gives a false picture of how many people are expected to use individual libraries in Ontario. The median tells us that libraries are being established to service far fewer than 24,000, with 11,000 being closer to the average. This median value shows that the tendency of the distributions is to center around 11,000, and divides the distribution in two. Since the median shows us how similar individual values are to each other, and what a typical value is, it would appear that as of 1994, there were too many libraries in Ontario serving too few people. It would be nice if there was a library every two miles, but that is very unrealistic, and money constraints will force some tough decisions to be made in the future. If the median is 11,000, and a large portion of the population does not even use the library, the actual numbers serviced on a daily basis are much less.
The same can be said of the holdings figures, which show that the mean is 75,824, and the median 35,183. The median gives a clearer picture of what is going on in the sample, because it is not being pulled away from the center of the distribution. Therefore, the average number of books per library is 35,000, no matter how many people are being served. They are not spread evenly over the system.
Per capita figures have a mean and median which are very close numerically, and infer that the average volumes per capita falls between three and four. This seems like a respectable figure, but this writer stresses that studying the data on an individual basis shows a truer picture of how the library system seems to cater to some libraries, with per capita figures reaching ten.
Besides presenting how distribution values are similar, analysts are also interested in finding out how they are different. This is done by calculating measures of dispersion, which indicate the extent that data is away from the center of a distribution (Walsh 1990,44). One such measure is standard deviation, or the average deviation of cases from the mean. If the standard deviation is large, it indicates that the values are scattered, while smaller measures reflect no variability in the distribution (Walsh 1991,43). In the data presented for population, the standard deviation is much higher than the mean. As A. Walsh writes in Statistics for Social Sciences, "what this means practically is that the mean is a poor indicator of the central tendency of this distribution" (Walsh 1990,43). The same phenomenon is seen in the holdings data to a much greater degree, with the mean sitting around 75,000, and the standard deviation at 156,339. In per capita, the standard deviation is much lower than the mean, and thus proves that the mean was the appropriate measure for those figures.
It looks as if some of the policies of the Ontario Public Library System need to be reviewed and some changes carried out to serve the people better to make sure that most of the libraries will be around for a long time, helping to educate society.
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O'Sullivan, E. and G.R. Rassel (1995). Research Methods for Public Administrators, 2nd ed. New York: Longman.
Rowntree, Derek (1991). Statistics Without Tears: A Primer for Non-Mathematicians. London, England: Penguin Books.
Walsh A. (1990). Statistics for the Social Sciences: With Computer Applications. New York: Harper & Row.