FutureStarr

A Stem and Leaf Plot With Thousands

# Stem and Leaf Plot With Thousands

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.

### Set

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 15–150 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.

One simple graph, the stem-and-leaf graph or stemplot, comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of a final significant digit. For example, [latex]23[/latex] has stem two and leaf three. The number [latex]432[/latex] has stem [latex]43[/latex] and leaf two. Likewise, the number [latex]5,432[/latex] has stem [latex]543[/latex] and leaf two. The decimal [latex]9.3[/latex] has stem nine and leaf three. Write the stems in a vertical line from smallest to largest. Draw a vertical line to the right of the stems. Then write the leaves in increasing order next to their corresponding stem. (Source: courses.lumenlearning.com)

### Value

One way to make data more usable is to make a stem-and-leaf plot. The digit(s) in the greatest place value(s) of the data values are the stems. The digits in the next greatest place values are the leaves. For example, if all the data are two-digit numbers, the number in the tens place would be used for the stem. The number in the ones place would be used for the leaf.

Stemplots are similar to histogram with the difference that in histogram, bars are used to compare data and in case of stemplots leaves represents actual numbers to be compared. Stemplots are also called stem and leaves plot as there is one step with largest place value digits on the left and at leaf(ves) to the right. A Stemplot is used to draw quantitative data with fewer than 50 observations. (Source: www.tutorialspoint.com)

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