Stem & leaf: mode median range
for 8th grade

Stem and leaf diagrams: mode, median, range

A stem and leaf diagram is a way of displaying a data set that shows the range of data in tabular form. Each data point is split into two parts, often splitting the first digit (the stem) from the remaining digit or digits (the leaf). This allows for a graphical division of the data into groups based on stems, with individual data points distinguished by their leaves. Stem and leaf diagrams can also be used for decimal numbers by splitting on the decimal point.

Stem and leaf diagrams make it relatively easy to find the mode, median and range for a data set. To find the mode from a stem and leaf diagram, look for the leaf value that appears most often in one row (do not count leaves from different rows as these are not the same value). The modal value is the most common leaf within one row combined with the stem according to the rule given by the diagram key.

To find the median value in a stem and leaf diagram, you should ensure that the diagram is ordered (stem values ascending from top to bottom, leaf values ascending from left to right). Then, count all the leaves in all the rows, and divide that number + 1 by 2. So if there are 15 leaves, the median value is at position (15 + 1) / 2 = 8. Count along all the leaves to the eighth leaf and read off the value as above by combining it with the stem value. If the median position falls between two leaves, calculate the median leaf value by adding the two values and dividing by two before combining it with the stem value.

To find the range of a stem and leaf diagram, take away the smallest value (stem and leaf) from the largest value (stem and leaf).

In this topic you are asked to calculate the mode, median or range of a series of stem and leaf diagrams. You will learn how useful these diagrams are for quickly deriving these values due to the way the data is laid out. There are 6 question/answer pairs in the lessons for this topic, and an additional 10 question/answer pairs in all the games and tests.