# Interpret the key results for Stem-and-Leaf Plot

Complete the following steps to interpret a stem-and-leaf plot.

## Step 1: Assess the key characteristics

Examine the center and spread of the distribution. Assess how the sample size may affect the appearance of the stem-and-leaf plot.

### Center and spread

Counts and median
The counts are in the first column on the left. The count for the row that contains the median value is enclosed in parentheses. The values for rows above and below the median are cumulative. The count for a row above the median represents the total count for that row and all the rows above it. The value for a row below the median represents the total count for that row and all the rows below it.
Data values

For each row, the number in the "stem" (the middle column) represents the first digit (or digits) of the sample values. The "leaf unit" at the top of the plot indicates which decimal place the leaf values represent.

The first row of the stem-and-leaf plot of Wait times has a stem value of 8 and contains the leaf values 0, 2, and 3. The leaf unit is 1. Thus, the first row of the plot represents sample values of approximately 80, 82, and 83.

The spread shows how much your data vary.

The following stem-and-leaf plot shows customer wait times. The median is in the row that has values between 95 and 99. The values range from 80 to 119.

 Stem-and-leaf of Wait times, N = 50 Leaf Unit = 1
 3 8 023 8 8 56688 21 9 0111111222444 (6) 9 555799 23 10 0000111233 13 10 55667789 5 11 14 3 11 579

Investigate any surprising or undesirable characteristics. For example, the stem-and-leaf plot of customer wait times showed a wider that expected spread. An investigation revealed that a software update caused instability and delays.

### Sample size (N)

The sample size can affect the appearance of the graph. The sample size is displayed at the top of the stem-and-leaf plot. In the previous example, the sample size is 50 (N=50).

Because a stem-and-leaf plot represents each data value, it is best when the sample size is less than approximately 50. If the sample is greater than 50, the data points on the plot may extend too far, and the distribution may be difficult to assess. If you have more than 50 data points, consider using Boxplot or Histogram.

## Step 2: Look for indicators of nonnormal or unusual data

Skewed data and multi-modal data indicate that data may be nonnormal. Outliers may indicate other conditions in your data.

### Skewed data

When data are skewed, the majority of the data are located on the high or low side of the graph. Skewness indicates that the data may not be normally distributed. Often, skewness is easiest to detect with a histogram or a boxplot.

The following stem-and-leaf plots are skewed. The stem-and-leaf plot with right-skewed data shows wait times. Most of the wait times are relatively short, and only a few wait times are long. The stem-and-leaf plot with left-skewed data shows failure time data. A few items fail immediately and many more items fail later.

Some analyses assume that your data come from a normal distribution. If your data are skewed (nonnormal), read the data considerations topic for the analysis to make sure that you can use data that are not normal.

### Outliers

Outliers, which are data values that are far away from other data values, can strongly affect your results. Often, outliers are easiest to identify on a boxplot. On a stem-and-leaf plot, isolated values at the ends identify possible outliers. For example, on the following stem-and-leaf plot, the last value at the bottom of this plot could be an outlier.

Try to identify the cause of any outliers. Correct any data-entry errors or measurement errors. Consider removing data values that are associated with abnormal, one-time events (special causes). Then, repeat the analysis.

### Multi-modal data

Multi-modal data have multiple peaks, also called modes. Multi-modal data often indicate that important variables are not yet accounted for.

If you have additional information that allows you to classify the observations into groups, you can create a group variable with this information. Then, you can create the graph with groups to determine whether the group variable accounts for the peaks in the data.

For example, a manager at a bank collects wait time data and creates a simple stem-and-leaf plot. The stem-and-leaf plot appears to have two peaks. Upon further investigation, the manager determines that the wait times for customers who are cashing checks is shorter than the wait time for customers who are applying for home equity loans. The manager adds a group variable for customer task, and then creates a stem-and-leaf plot with groups. The stem-and-leaf plot with groups shows that the peaks correspond to the two groups.
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