# Glossary

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```					Handout 5

Glossary
This is a brief glossary of the terms used in the Management Math for Libraries workshop. Average – a measure of central tendency or mid-point in a data distribution. Can be mean, median, or mode. Break even analysis – the technique used to find the point where total costs equal total revenues. Categorical data – captures qualities or characteristics (gender, age, race, language spoken at home, etc. May be referred to as qualitative data. Numerical data has meaning as a measurement (height, weight, IQ, blood pressure, etc.) and is referred to as quantitative data. Confidence interval – range around which an actual value for the population is likely to fall. Same as margin of error. For example, if a poll reports that 45% of likely voters plan to vote for John Kerry and that the confidence interval is +/- 5%, that means the range of votes for Kerry would be 40-50%. Confidence level – tells you how sure you can be, how often the true percentage of the population would pick an answer within the confidence interval. 95% is often used. Correlation – measures the strength of the relationship between two sets of data (two variables). Remember: correlation is not cause and effect. Two variable may move in a related way but that doesn’t mean thee is a cause and effect relationship between them. Cost benefit analysis – a decision-making technique to develop quantitative information on how to allocate resources. Descriptive statistics – a method for summarizing, organizing, and presenting information, a collection of procedures or techniques that can be used to make sense out of numbers. These tools include: percents, tables, graphs, frequency distributions, measures of central tendency (averages), measures of variability (dispersion), linear regression equations, and correlation coefficients. “Inferential statistics” is the second broad class of statistics and consists of methods that go beyond information summary. The aim of inferential statistics is to make broad generalizations based on limited studies (samples). Distribution – a set of related values (e.g., circulation, questions answered, salaries). A distribution is described by its mid-point (average), a measure of spread, and a measure of its shape.

Management Math for Libraries Winter 2004-05 - This material has been created by Jeanne Goodrich for the Infopeople Project [infopeople.org], supported by the U.S. Institute of Museum and Library Services under the provisions of the Library Services and Technology Act, administered in California by the State Librarian. Any use of this material should credit the author and funding source.

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Handout 5

Forecasting – Predicting the future. Data analysts often use trends and time series as the basis for their predictions. This may not be a good idea. Histogram – a type of bar chart used to depict data’s shape and distribution. Kurtosis – the flatness or pointedness (sometimes called peakedness) of a distribution. Again, easy to see if the data’s shape is shown. This is at the most esoteric level of data analysis. Math anxiety – A feeling of intense frustration or helplessness about one’s ability to do math. Often referred to as math phobia. Mean – arithmetic average, sum of all values divided by the number of values in the data set. The mean is often what people mean by “average” but it is sensitive to extreme values, so may be misleading. Median – the value in the middle of a data series. Often more representative of a range of values, particularly if there is great variance. Mode – the value occurring most often in a data series. This kind of average describes the relative popularity of specific values. It is the only appropriate measure for categorical values (hair color, gender, educational degree, etc.). Nonprobability sample – a sample in which each element in the population does not have an equal chance of inclusion. The sample, therefore, will not be accurately predictive of the population as a whole. Numerical data – Data that have meaning as measurements, numbers you collect through measurements of various kinds. Outcome measure – a measure of effectiveness, of results achieved. Answers the question: What difference did our program or service make to the participant or user? Output measure – a measure of volume, amount of work produced or work products produced. Percent – literally means “per hundred.” Shows the relative size of two or more numbers. Because percents are converted to a scale based on 100, a percent is a fraction in which the denominator is always 100. Percentiles – numbers that divide a set of ranked data into 100 equal parts; the most widely used statistical measure of relative position in a distribution, especially used to describe a large data set. Quartiles divide data into four parts and deciles into ten parts. Performance measurement – a way to produce objective, relevant information on program or organization performance.

Management Math for Libraries Winter 2004-05 - This material has been created by Jeanne Goodrich for the Infopeople Project [infopeople.org], supported by the U.S. Institute of Museum and Library Services under the provisions of the Library Services and Technology Act, administered in California by the State Librarian. Any use of this material should credit the author and funding source.

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Handout 5

Probability sample – is a sample in which each element in the population has an equal chance of inclusion. Range – the distance between the lowest and highest values in a data set. Rate – a ratio that reflects some quantity per a certain unit. For example, circulation of 4.5 per capita. Ratio – a fraction that divides to quantities. For example, 3 girls to 2 boys is a ration of 3:2. Regression analysis – a way of defining the extent to which two variables are related. Can be used in an attempt to predict causes or changes between variables. While in regression the emphasis is on predicting one variable from the other, in correlation the emphasis is on the degree to which a linear model may describe the relationship between two variables. In regression the interest is directional, one variable is predicted and the other is the predictor; in correlation the interest is non-directional, the relationship is the critical aspect. Return on investment – a calculation that represents the percentage of return (a ratio) from the capital investment made in a project or activity. The ROI is calculated by dividing the annual net profit by the cost of project investment. Sampling – process whereby items are selected from a population; in order to generalize finding to the full population, samples should be representative of the population and large enough to reflect the population. Shape – data can be presented graphically, usually in a histogram, to show its shape and whether its symmetrical or lop-sided. Skew – lopsidedness in a distribution. Easy to see in a histogram. Spread – The range of values in a distribution; also known as scatter and dispersion. Standard Deviation – a measure of the spread of a set of numbers, a better measurement than range. Standard deviation summarizes the degree to which the numbers in the distribution differ from the mean. Statistical significance – probably true, small probability of happening just by chance. For example, if a drug is found to be more effective at treating breat cancer than the current treatment is, researchers say that the new drug shows a statistically significant improvement in the survival rate of patients with breast cancer. Trend – The long-run path of a time series (a record of developments over time). Shows general movement. Z Score – shows the position of a particular data element relative to the mean; the number of standard deviations above or below the mean a value is.
Management Math for Libraries Winter 2004-05 - This material has been created by Jeanne Goodrich for the Infopeople Project [infopeople.org], supported by the U.S. Institute of Museum and Library Services under the provisions of the Library Services and Technology Act, administered in California by the State Librarian. Any use of this material should credit the author and funding source.

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