The quartiles are 71.5 and 84.5, meaning that the middle 50% of the observations fall between these two scores. The mode, the most frequently occurring observation, is 75, like the median. The median is 75, so 50% of the observations scored below 75 and 50% scored above 75. The midterm exam scores range from 92-65. It appears to show a normal curve, with no real outliers. Let’s take the digits in the tens position as the stems and the digits in the ones position as the leaves. Since there are relatively few observations, a stem plot would be easy to sketch out and can be useful for describing the general shape of the distribution as well as to find other descriptive statistics.Ħ5, 67, 68, 70, 71, 71, 72, 73, 73, 74, 74, 75, 75, 75, 77, 79, 81, 81, 84, 85, 85, 89, 89, 90, 92 In this example, we have a set of AP® Statistics midterm exam scores. Let’s go through examples of how to create stem plots and how to interpret them. Also take note of the general shape of the distribution. When interpreting a stem plot you want to find the range, median, quartiles, and interquartile range. Is the data normally distributed? Is it shaped like a bell curve? You should be able to identify the range, the median, the quartiles, as well as any potential outliers.įinally, the stem plot should also give you an idea of the shape of the distribution of the data. So if you have a value of 25, 2 is the stem that goes on the left of the vertical line and 5 is the leaf that goes on the right.įrom the stem plot it should be easy to describe the distribution of the data. The stems are usually the first digit of a number. The stems are on the left of the vertical line and the leaves are on the right. In a stem plot you have a vertical line dividing the stems from the leaves. Now that we know what stem plots are and how they are useful, how do we actually construct a stem plot? What do we do with a stem plot, or how do we interpret it? Steps to Interpreting a Stem Plotįirst you should know how to construct a stem plot. It would be quite cumbersome to plot out by hand hundreds of values. However, as you can probably guess, a main disadvantage of the stem plot is that it is really only useful with relatively small data sets. The primary advantage of a stem plot is that rather than condensing our data into points or into bars on a graph, we can see the original numerical values of the data. Other ways to summarize univariate data include a histogram and pie chart. The stem plot is one method of summarizing univariate data visually. Most importantly, the stem plot is useful because it can help with finding the median, mode, and quartiles of data, the range, minimum and maximum values, as well as the most and least frequently occurring observed values in the data. Because in AP® Statistics we are interested in normally distributed data, or a bell curve distribution, the stem plot is an easy and fast way to get a general feel of the distribution especially if the data has relatively few observations. The stem-and-leaf plot or stem plot, for short, is a way to quickly create a graphical display of quantitative data to get an idea of its shape. There are many different ways to get to know data, and you are probably most familiar with calculating central tendencies and measures of dispersion.Īnother thing we are interested in when describing data is its shape, which can be important for determining whether a variable is appropriate for a particular analysis later on. This is done so that you can get to know your data, find errors in data collection and data entry, and to find out basic information such as the central tendencies and dispersion characteristics of data. In statistics, descriptive data analysis must always be done first before anything else.
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