# In statistics when to use stem and leaf or histogram pdf

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## Stem-and-leaf display

A stem-and-leaf display or stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram , to assist in visualizing the shape of a distribution. They evolved from Arthur Bowley 's work in the early s, and are useful tools in exploratory data analysis. Stemplots became more commonly used in the s after the publication of John Tukey 's book on exploratory data analysis in Modern computers' superior graphic capabilities have meant these techniques are less often used.

This plot has been implemented in Octave [2] and R. A stem-and-leaf plot is also called a stemplot , but the latter term often refers to another chart type. A simple stem plot may refer to plotting a matrix of y values onto a common x axis, and identifying the common x value with a vertical line, and the individual y values with symbols on the line.

Unlike histograms, stem-and-leaf displays retain the original data to at least two significant digits, and put the data in order, thereby easing the move to order-based inference and non-parametric statistics. To construct a stem-and-leaf display, the observations must first be sorted in ascending order: this can be done most easily if working by hand by constructing a draft of the stem-and-leaf display with the leaves unsorted, then sorting the leaves to produce the final stem-and-leaf display.

Here is the sorted set of data values that will be used in the following example:. Next, it must be determined what the stems will represent and what the leaves will represent. Typically, the leaf contains the last digit of the number and the stem contains all of the other digits. In the case of very large numbers, the data values may be rounded to a particular place value such as the hundreds place that will be used for the leaves.

The remaining digits to the left of the rounded place value are used as the stem. In this example, the leaf represents the ones place and the stem will represent the rest of the number tens place and higher. The stem-and-leaf display is drawn with two columns separated by a vertical line.

The stems are listed to the left of the vertical line. It is important that each stem is listed only once and that no numbers are skipped, even if it means that some stems have no leaves. The leaves are listed in increasing order in a row to the right of each stem. It is important to note that when there is a repeated number in the data such as two 72s then the plot must reflect such so the plot would look like 7 2 2 5 6 7 when it has the numbers 72 72 75 76 Rounding may be needed to create a stem-and-leaf display.

Based on the following set of data, the stem plot below would be created:. Non-integers are rounded. This allowed the stem and leaf plot to retain its shape, even for more complicated data sets. As in this example below:. Stem-and-leaf displays are useful for displaying the relative density and shape of the data, giving the reader a quick overview of the distribution. They retain most of the raw numerical data, often with perfect integrity. They are also useful for highlighting outliers and finding the mode.

However, stem-and-leaf displays are only useful for moderately sized data sets around 15— data points. With very small data sets a stem-and-leaf displays can be of little use, as a reasonable number of data points are required to establish definitive distribution properties.

A dot plot may be better suited for such data. With very large data sets, a stem-and-leaf display will become very cluttered, since each data point must be represented numerically. A box plot or histogram may become more appropriate as the data size increases.

From Wikipedia, the free encyclopedia. They do not create a stem-and-leaf display. Outline Index. Descriptive statistics. Mean arithmetic geometric harmonic Median Mode. Central limit theorem Moments Skewness Kurtosis L-moments. Index of dispersion. Grouped data Frequency distribution Contingency table. Data collection. Sampling stratified cluster Standard error Opinion poll Questionnaire.

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Bayesian probability prior posterior Credible interval Bayes factor Bayesian estimator Maximum posterior estimator. Correlation Regression analysis. Pearson product-moment Partial correlation Confounding variable Coefficient of determination. Simple linear regression Ordinary least squares General linear model Bayesian regression. Regression Manova Principal components Canonical correlation Discriminant analysis Cluster analysis Classification Structural equation model Factor analysis Multivariate distributions Elliptical distributions Normal.

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## Stem and leaf plots review

A stem-and-leaf display or stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram , to assist in visualizing the shape of a distribution. They evolved from Arthur Bowley 's work in the early s, and are useful tools in exploratory data analysis. Stemplots became more commonly used in the s after the publication of John Tukey 's book on exploratory data analysis in Modern computers' superior graphic capabilities have meant these techniques are less often used. This plot has been implemented in Octave [2] and R. A stem-and-leaf plot is also called a stemplot , but the latter term often refers to another chart type. A simple stem plot may refer to plotting a matrix of y values onto a common x axis, and identifying the common x value with a vertical line, and the individual y values with symbols on the line.

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A random sample of 64 people were selected to take the Stanford-Binet Intelligence Test. After each person completed the test, they were assigned an intelligence quotient IQ based on their performance on the test. The resulting 64 IQs are as follows:.