How Do Colorado Public Libraries Stack Up?

From social media, to sports, to books and everything in between, almost anything can be compared these days. Of course, comparisons can be good or bad, healthy or unhealthy, incredibly insightful or harmful and misleading. This is all true in research as well; however, there’s no escaping that comparisons are a central component of data analysis, so it’s important to know how to make them correctly. In this post we are going to explore percentiles, which are one of the most universally understood ways to draw comparisons from a data set. We will then use percentiles to compare Colorado public library data to data from across the nation and finally, visualize the spread of this data in a box and whisker plot.

What’s a Percentile?

Percentiles are a way to measure how a value compares to all the other values in a data set. To calculate percentiles a data set must be made up of or transformed into quantitative data that can be ordered from the smallest to largest value. Regardless of how many total numbers are in a data set, all the data points will have a percentile rank ranging from 0 to 100 which indicates where the point falls in relation to all other values in that data set. A value’s percentile tells us the percent of values in the data set that are less than or equal to that particular value. The closer a data point is to the minimum value in the set the closer its percentile will be to 0, and the closer a data point is to the maximum value in the set the closer its percentile will be to 100. For example, if a value is in the 75th percentile, that means that 75% of the values in that data set are equal to or lower than this value. Likewise, if a child is in the 90th percentile for height that means that they are taller than 90% of children their age.

State Percentiles for Public Libraries

Before moving forward, let’s ground this explanation of percentiles in some real world public library data. The Institute of Museum and Library Services (IMLS) compiles all the data from the Public Library Surveys (PLS) across the nation, making it possible to find Colorado’s percentile rank for multiple pieces of public library data. By using the 2021 data from the IMLS PLS benchmarking tables and Excel’s percentile rank formula I found that, when compared to all 50 states and the District of Columbia, Colorado ranks above the 85th percentile for the following measures: Circulation per capita (96th percentile), Registered users per capita (96th percentile), Revenue per capita (92nd percentile), and Expenditures per capita (86th percentile). The full data set is included in a table at the end of this post…

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