SKILLS ...............................................
Stem-and Leaf and Box and Whiskers Plots

A stem-and-leaf plot is a display that organizes data to show its shape and distribution.

In a stem-and-leaf plot each data value is split into a "stem" portion and a "leaf" portion. The "leaf" is usually the last digit of the number and the other digits to the left of the "leaf" form the "stem". The number 42 would be split apart, with the stem becoming the 4 and the leaf becoming the 2.

Constructing a stem-and-leaf plot:

The data: Major League base-running times in seconds: 2.9, 3.2, 3.9, 4.0, 4.0, 4.1, 4.1, 4.1, 4.2, 4.2, 4.2, 4.2, 4.3, 4.4, 4.5, 4.6, 4.8, 4.9, 5.0, 5.6, 6.1

If data are not in numerical order, the next steps are easier. However, this is NOT a required step.

Now, separate each number into a stem and a leaf. Since these are two digit numbers, the units digit is the stem and the tenth digit is the leaf. The data point 3.8 is represented as Stem Leaf

3. 8

Group numbers that have the same stems. List the stems in numerical order. (Place leaf values in increasing order.)

Running Times

Stem Leaf

2. 9

3. 2 9

4. 0 0 1 1 1 2 2 2 2 3 4 5 6 8 9

5. 0 6

6. 1

A stem-and-leaf plot shows the shape and distribution of data. It can be clearly seen in the diagram above that the data clusters around the row with a stem of 4.

Constructing a box-and-whiskers plot

A box-and-whisker plot is a useful way to display data values. It allows people to see data and to draw conclusions as they compare two or more data sets.

A box-and-whisker plot shows only certain data values. It turns all of the data into a summary that shows only five data points.

The five points are the median, the upper and lower quartiles, and the smallest and greatest values in the distribution.

The first step in constructing a box-and-whisker plot is to first find the median, the lower quartile and the upper quartile of a given set of data.

Example: Look at the numbers we used above.

First, find the median. The median is the value exactly in the middle of an ordered set of numbers.

In this data set:

2.9, 3.2, 3.9, 4.0, 4.0, 4.1, 4.1, 4.1, 4.2, 4.2, 4.2, 4.2, 4.3, 4.4, 4.5, 4.6, 4.8, 4.9, 5.0, 5.6, 6.1

4.2 is the median

Next, consider only the values to the left of the median:

2.9, 3.2, 3.9, 4.0, 4.0, 4.1, 4.1, 4.1, 4.2, 4.2,.

Find the median of this set of numbers. Remember, the median is the value exactly in the middle of an ordered set of numbers. Since there is no single number in this set, the median is the average of the two middle numbers. Thus 4.05 is the median here, and is called the lower quartile.

4.05 is the lower quartile

Now consider only the values to the right of the median:

4.2, 4.3, 4.4, 4.5, 4.6, 4.8, 4.9, 5.0, 5.6, 6.1

We now find the median of this set of numbers. The median is between 4.6 and 4.8, 4.7 is called the upper quartile.

4.7 is the upper quartile

A box and whisker plot is built from the median, the upper quartile, the lower quartile and the two extremes in the data.

2........3..........4..........5.........6