Stem and Leaf Plots

Stem and leaf plots are a simple and effective way to organize and display data. It displays numerical data by splitting it into a stem and a leaf. Generally, the leading digit or digits represent the stem, and the last digit represents the leaf. By splitting each number into a "stem" and a "leaf," this method provides a clear and concise view of numerical data.

In this article, we will discuss the concept of stem and leaf plots in detail, including their key features, methods to create the plot, and various solved and unsolved examples.

What are Stem and Leaf Plots?

A stem and leaf plot is a graphical representation used to organize and display quantitative data in a semi-tabular form. It helps in visualizing the distribution of the data set and retains the original data values, making it easy to identify the shape, central tendency, and variability of the data.

A stem and leaf plot splits each data point into a "stem" and a "leaf." The "stem" represents the leading digits, while the "leaf" represents the trailing digit. This separation makes it easy to organize data and see patterns.

For example: For the data set: 23, 25, 27, 32, 34, 35, 41, 42

• Stems: 2, 3, 4
• Leaves: 3, 5, 7 | 2, 4, 5 | 1, 2

This data can be represented as following table:

Stem	Leaves
2	3, 5, 7
3	2, 4, 5
4	1, 2

Key Features of Stem and Leaf Plots

Some of the key features of steam and leaf plots are:

• Stem and leaf plots display numerical data by splitting each data point into a "stem" (usually the first digit or digits) and a "leaf" (usually the last digit).
• The stems are listed vertically, and the leaves are written next to their corresponding stem in numerical order.
• A key is provided to explain what the stem and leaf represent for that particular plot.
• Stem and leaf plots are useful for displaying the shape, spread, and central tendency of a data distribution. They can highlight outliers and help identify the mode.
• Stem and leaf plots retain the original data values, unlike histograms, which only show summary information.
• Stems with no leaves are still included to preserve the horizontal axis scaling and highlight gaps in the data.

How to Create Stem and Leaf Plots?

To create the stem and leaf plot of any data set, we can use the following steps:

Step 1: Arrange your data set in ascending order.

Step 2: Identify the "stems" by separating the leading digits of the numbers in your data set.

• For example, if your data includes numbers like 23, 25, and 27, the stem would be 2.

Step 3: Identify the "leaves" by taking the trailing digits of the numbers.

• For instance, in the number 23, the leaf would be 3.

Step 4: Write down the stems in a vertical column.

Step 5: Next to each stem, write down the corresponding leaves in ascending order.

This will result in the tabular represetation of data known as stem and leaf plot.

How to Read Stem and Leaf Plot?

Let's consider a given stem and leaf plot i.e.,

Stem	Leaves
2	3, 5, 7
3	2, 4, 5
4	1, 2

To read the data from this plot, we can combine each stem and leaf as follows:

• For the stem "2" with leaves "3, 5, 7":
  • Combine: 23, 25, 27
• For the stem "3" with leaves "2, 4, 5":
  • Combine: 32, 34, 35
• For the stem "4" with leaves "1, 2":
  • Combine: 41, 42

Stem and Leaf Plot With Decimals

When dealing with data that includes decimal values, the process of creating a stem and leaf plot remains similar. The key difference is in how you determine the stems and leaves. For data with decimal numbers

• Stems: The integer part of each number.
• Leaves: The decimal part of each number.

Lets consider an example for better understanding.

Consider data set: 2.3, 2.5, 2.7, 3.2, 3.4, 3.5, 4.1, 4.2

• Stems: 2, 3, 4
• Leaves: 3, 5, 7 | 2, 4, 5 | 1, 2

This can be represented in the form of table as follows:

Stem	Leaves
2	3, 5, 7
3	2, 4, 5
4	1, 2

Conclusion

In conclusion, stem and leaf plots are a simple yet powerful tool for visualizing data. They help in quickly identifying the shape, spread, and central tendency of a dataset. By organizing data in a structured format, these plots make it easy to see patterns and outliers. Whether for educational purposes or data analysis, stem and leaf plots offer a clear and concise way to understand numerical data.

Read More,

• Bar Graph
• Double Bar Graph
• Pie Chart
• Tally Marks

Solved Examples on Stem and Leaf Plots

Example 1. A school teacher measured heights (in cm) of the students in a classroom. The values are given below.

152, 157, 165, 168, 158, 172, 179, 175, 185, 188, 192, 190

Draw a stem-and-leaf diagram to represent the given data.

Solution:

The given data values are 152, 157, 165, 168, 158, 172 , 179, 175, 185, 188, 192, 190

Here, first two digits are the stem and the last digit is leaf.

As example, 152 = 15 I 2 (15 stem and 2 leaf).

We can get the data in ascending order such as :

152, 157, 158, 165, 168, 172, 175, 179, 185, 188, 190, 192.

Now, place this data values in a tabular form or a stem and leaf diagram.

Stem	Leaf
15	2, 7, 8
16	5, 8
17	2, 5, 9
18	5, 8
19	0, 2

Example 2. Given below is the stem and leaf plot:

Stem	Plot
1	0, 3, 7
2	2, 5
3	1
4	5, 8

a) What are the data values of stem 4?

b) How many values are less than 17?

Solution:

a) The corresponding leaf values of stem 4 are 5 and 8.

So, the data values of stem 4 are 45 and 48.

b) The corresponding leaf values of stem 1 are 0, 3 and 7.

The data values of stem 1 are 10, 13 and 17.

10 and 13 are the less values than 17.

Therefore, the two values are less than 17.

Practice Problems on Stem and Leaf Plots

Problem 1: Construct a stem and leaf plot for the following data set:

56, 59, 61, 62, 65, 68, 71, 72, 75, 78

Problem 2: Given the stem and leaf plot, reconstruct the original data set:

Stem	Leaves
4	1, 2, 5, 8
5	0, 3, 4, 7
6	2, 4, 5, 9

Problem 3: Create a stem and leaf plot for the following data:

33.1, 34.5, 35.0, 36.8, 37.3, 38.2, 39.7, 40.5, 41.1

Problem 4: Create a stem and leaf plot for the following data set:

103, 105, 107, 109, 112, 115, 118, 121, 124, 127