Stem and Leaf Plot

A stem and leaf plot is a graphical representation of numerical data that helps in organizing and analyzing values while preserving the dataset that was given.

It separates each number into a stem and a leaf, which makes it easier to identify trends like distributions, median, and mode. We use stem and leaf plots in education, business, and statistics to quickly interpret numerical data.

The key features are given below:

• Stem and leaf plots display numerical data by splitting each data point into a stem and a leaf

• The stems are listed vertically, and the leaves are listed next to their corresponding stem in numerical order.

• A key is provided on how to read the stem and leaf plot

• They are useful for displaying the shape, spread, and central tendency of a data distribution.

• They retain the original values.

• Stems without leaves are included to preserve the horizontal axis scaling and highlight gaps in the data. 

Here, we will learn how to create a stem and leaf plot and also learn how to split the stem and leaf plot. We will also learn what does splitting of stem and leaf plots means and how it is done:

How to Create Stem and Leaf Plots?

To create a stem and leaf plot, we have to follow the following steps:

Step 1: Organize the Data:  

 
First, we have to collect and list all the numerical values in the dataset. Then we have to check and ensure that all the numbers are accurate. For example, the dataset:
23, 45, 31, 37, 29, 42, 34, 47, 38, 51.

Step 2: List the Data Set in Ascending Order:
Next, we have to arrange the values in ascending order:
23, 29, 31, 34, 37, 38, 42, 45, 47, 51

Step 3: Identify the Stems and Leaves:
Next, we have to identify the stems and leaves:
Stems = 2, 3, 4, 5
Leaves = 2 (3, 9), 3 (1, 4, 7, 8), 4(2, 5, 7), 5 (1)

Step 4: List the Stems:

Step 5: Add the Leaves:

Step 6: Include a Legend:
Lastly, include a legend where it says that “2| 3 9” reads as 23 and 29 for all the stems and leaves.

The split of the stem and leaf plot splits each stem into many stems based on the frequency. We place the smaller leaves on the first part of the split stem and the larger leaves on the subsequent stems.

For example, let us consider the dataset:

78, 82, 82, 90, 90, 95, 95, 96, 97, 98, 98, 98

The stem and leaf plot for the above data set is as follows:

The split stem and leaf plot is as follows:
 

Let us now see how to construct a stem and leaf plot:
To construct a stem and leaf plot, we have to follow the following steps:

Step 1: First, we have to look at the given data and find the number of digits. Then, we have to classify them as 2 or 3-digit numbers.

Step 2: After that, we have to fix the stem and leaf plot key or legend.

Step 3: Then, we have to identify the first digits as stems and the last digits as leaves.

Step 4: Then, determine the range of the data, which means the lowest and highest values among the data.

Step 5: Draw a vertical line. Place the stem on the left column and the leaf on the right column.

Step 6: List the stems in the stem column. Arrange the stems in ascending order, starting from the lowest to the top.

Step 7: Plot the leaves in the leaf column against the stem from lowest to highest horizontally.

When we deal with data that has decimals, the process of creating a stem and leaf plot is similar. The difference is in how we determine the stems and leaves. For example,

For the given data set, create a stem and leaf plot:

2.3, 2.5, 2.7, 3.2, 3.4, 3.5, 4.5, 4.7, 4.9.

The stems in the above data set are the integers: 2, 3, 4

The leaves in the above data set are numbers after the decimal points

To represent the data, see the table given below:

There are many uses of stem and leaf plots. Let us now see the uses and applications of stem and leaf plots in different fields:

• Education: The stem and leaf plots are used in education, where teachers use stem and leaf plots to analyze students’ test scores and identify trends. It helps to determine class performance, median, mode, and overall grade distribution.

• Business and Sales Analysis: We use stem and leaf plots in business and sales analysis, where businesses use them to analyze daily, weekly, and monthly sales data. It also helps in identifying trends, peak sales periods, and performance comparisons.

• Sports Statistics: In sports statistics, we use stem and leaf plots to analyze them to summarize player performance. It also helps in comparing athletes’ progress over time.