Question

Each observation in the following data set is the number of housing units (homes or condominiums) sold during November 1992 in a region corresponding to a particular Orange County, California, ZIP code: \(\begin{array}{lllrrrrrrrrr}25 & 18 & 16 & 6 & 26 & 11 & 29 & 7 & 5 & 15 & 12 & 37 \\ 35 & 11 & 16 & 35 & 20 & 27 & 17 & 30 & 10 & 16 & 28 & 13 \\ 26 & 11 & 12 & 8 & 9 & 29 & 0 & 20 & 30 & 12 & 45 & 26 \\ 21 & 30 & 18 & 31 & 0 & 46 & 47 & 14 & 13 & 29 & 11 & 18 \\ 10 & 27 & 5 & 18 & 67 & 21 & 35 & 48 & 42 & 70 & 43 & 0 \\ 30 & 17 & 35 & 40 & 61 & 18 & 17 & 17 & & & & \end{array}\) Construct a stem-and-leaf display, and comment on any interesting features.

Short answer

The stem-and-leaf display shows a wide-ranging set of housing sales with a distribution leaning slightly towards the lower sale numbers. Outliers can be noted at the high end of the scale, possibly indicating instances of significantly higher housing activity in certain regions.

Step-by-step solution

Understanding Stem-and-Leaf Display

A stem-and-leaf display or 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. Stems represent higher order places and leaves represent lower order places.

Creating the Stems

Stems will be values ranging from 0 to 7 (as the given data set ranges from 0 to 70), representing the tens place of the data.

Attaching the Leaves

For each observation in the data set, the units place is attached to its corresponding stem. For example, a data point of 35 means a leaf of 5 is attached to the stem 3. Repeat this for all observations in the data set.

Organizing the Stem-and-Leaf Plot

Organize the leaves in ascending order for each stem. Now, each stem combined with its leaves forms a number in the data set, and observing the table gives a visual representation of all the data.

Analysing the Data

The stem-and-leaf plot will allow a clear view of the distribution of the data, and one could potentially identify outliers, mode, or trends visually. This overview can help to interpret the patterns in the housing sale data.