How to Create and Read a Stem and Leaf Plot in Maths
Statistics need to be often displayed graphically to be able to read the data and analyse it easily. There are several ways to represent statistical data graphically. These include bar graphs, histograms, line graphs, column charts, line charts, pie charts, pivot tables, scatter charts, treemaps, stem and leaf plots, etc.
Displaying statistical data visually or Data visualization is a useful way to provide accessible ways to analyze patterns trends across a large set of data. These are used by data scientists, governments, climatologists, etc to record data and represent it graphically for easier analysis.
Stem and leaf plots are one such way of representing data in an easier and convenient way. Stem and leaf plots have several advantages that make them very handy for the purpose of analyzing large sets of data easily.
A basic understanding of different ways of data visualization comes in handy in all fields. Stem and leaf plots are a method of displaying data horizontally in two columns. They look very simple and can be used to display a huge set of data.
On this page, you will understand the meaning of stem and leaf plots. You will also get to know how these are plotted. You will be further introduced to another type of stem and leaf plot called the two-sided or back t back stem and leaf plot. We’ll also make Stem and Leaf Plots to display data distributions with the help of a few examples. In the given examples, you’ll get to know how to organize the data and to use the stem-and-leaf plot concept to obtain answers to interesting questions.
Lastly, any questions that you may have regarding the stem and leaf plots will also be answered. Refer to the official website of Vedantu or download the app for an elaborate and comprehensive explanation.
Stem and Leaf Plot Definition
The Stem and Leaf plot is a way of organizing data into a form that makes it easy to see the frequency of different values. In other words, we can say that a Stem and Leaf Plot is a table in which each data value is split into a “stem” and a “leaf.” The “stem” is the left-hand column that has the tens of digits. The “leaves” are listed in the right-hand column, showing all the ones digit for each of the tens, the twenties, thirties, and forties.
Remember that Stem and Leaf plots are a pictorial representation of grouped data, but they can also be called a modal representation. Because, by quick visual inspection at the Stem and Leaf plot, we can determine the mode.
Steps for Making Stem-and-Leaf Plots
First, determine the smallest and largest number in the data.
Identify the stems.
Draw a with two columns and name them as “Stem” and “Leaf”.
Fill in the leaf data.
Remember, a Stem and Leaf plot can have multiple sets of leaves.
Let us understand with an example:
Consider we have to make a Stem and Leaf plot for the data: 71, 43, 65, 76, 98, 82, 95, 83, 84, 96.
We’ll use the tens digits as the stem values and the one’s digits as the leaves. For better understanding, let’s order the list, but this is optional:
43, 65, 71, 76, 82, 83, 84, 95, 96, 98.
Now, let’s draw a table with two columns and mark the left-hand column as “Stem” and the right-hand column as “Leaf”.
The above is one of the simple cases for Stem and Leaf plots.
Here,
Stem "4" Leaf "3" means 43.
Stem "7" Leaf "6" means 76.
Stem "9" Leaf "6" means 96.
What if we Have to Make a Stem and Leaf Plot for Decimals?
If we have a number like 13.4, we will make “13” the Stem and “4” the Leaf. That’s right, the decimal doesn’t matter. Since the decimal will be in place of the vertical line separating the Stem and Leaf, we don’t have to worry about it.
Activity on Stem and Leaf Plot
Now that you have an idea about stem and leaf plots, can you answer the following questions, considering the data given? Let’s see.
What are the leaf numbers for stem 3?
What are the data values for stem 3?
What are the data values for stem 0?
List the data values greater than 30.
Solutions:
1. First, look at the left-hand “Stems” column and locate stem 3. Then we'll look at the corresponding numbers in the right-hand “Leaves” column. The numbers are 8 and 6.
2. Combining the stem value of 3 with the corresponding numbers 8 and 6 in the right-hand ''Leaves'' column, using the information in part (1) of the Question above, we found the following data values for stem 3 are 38 and 36.
3. The row where the stem = 1 gives us leaves = 4 and 5.
Hence, the data values are obtained by combining the stem and the leaves to get 14 and 15.
The data values are 14 and 15.
4. Starting with stem = 3, we have data values of 38 and 36. Moving on to stem 4, we get corresponding data values of 49, 41, 47 and 44. That brings us to the end of the stem-and-leaf plot.
So, the data values greater than 30, according to the list above, are 38, 36, 49, 41, 47 and 44.
Do You Know?
We can also combine and distribute data for two types of data. They are called Two-sided Stem and Leaf Plots, which are also often called back-to-back stem-and-leaf plots. With help of Two-sided Stem and Leaf Plots, we can determine Range, Median and Mode.
Other Alternatives apart from Stem and Leaf plots to organise and group data are:
Frequency distribution
Histogram
FAQs on Stem and Leaf Plots Made Easy
1. What is a stem-and-leaf plot and how does it function?
A stem-and-leaf plot is a method of organising numerical data based on place value. It visually groups data to show its distribution. The plot is split into two parts: the 'stem', which consists of the leading digit(s) of a data point, and the 'leaf', which is always the last digit. For example, in the number 45, '4' is the stem and '5' is the leaf. This method allows us to see individual data values while also getting an overview similar to a bar chart.
2. What are the key steps to create a simple stem-and-leaf plot?
Creating a stem-and-leaf plot involves a few straightforward steps:
Step 1: Identify the stems and leaves for all data points. The leaf is the last digit, and the stem is all preceding digits.
Step 2: Draw a vertical line. Write the stems in ascending order to the left of the line.
Step 3: For each data point, write its leaf on the right side of the line, next to its corresponding stem.
Step 4: Arrange the leaves for each stem in ascending order.
Step 5: Add a 'key' to explain how to read the plot (e.g., Key: 4|5 means 45).
3. Why is a 'key' essential in a stem-and-leaf plot?
A 'key' is crucial because it provides the context needed to interpret the plot correctly. It explains the place value and unit of the data. For instance, a stem of '12' and a leaf of '3' could mean 123, 12.3, or even 1.23. The key clarifies this ambiguity by giving a concrete example, such as 'Key: 12|3 = 12.3'. Without a key, the plot is just a collection of numbers with no clear meaning, making it impossible to understand the actual data values.
4. How is a stem-and-leaf plot different from a histogram?
While both a stem-and-leaf plot and a histogram show the distribution of data, they have a key difference. A histogram groups data into intervals (or bins) and only shows the frequency for each interval, so the original data values are lost. In contrast, a stem-and-leaf plot retains all the original data values. You can reconstruct the entire dataset from the plot, which allows for calculating the mean, median, and mode precisely, something not possible with a histogram alone.
5. What is the purpose of a back-to-back stem-and-leaf plot?
A back-to-back stem-and-leaf plot, also known as a double stem-and-leaf plot, is used to compare two different datasets side-by-side. It features a central stem column with leaves for one dataset branching to the left and leaves for the second dataset branching to the right. This format makes it very easy to visually compare the distribution, range, and median of the two groups simultaneously, such as comparing the test scores of two different classes.
6. What are some real-world examples where a stem-and-leaf plot is useful?
Stem-and-leaf plots are practical for displaying moderately sized datasets clearly. Some real-world applications include:
Displaying the test scores of students in a class to see the spread of marks.
Recording the daily temperatures over a month to analyse climate patterns.
Tracking the heights or weights of a group of people for a health survey.
Listing the ages of employees in a small company to understand the workforce demographics.
7. What are the main advantages and limitations of using stem-and-leaf plots?
Stem-and-leaf plots offer several benefits but also have drawbacks.
Advantages:
They show the exact data values, unlike histograms.
They display the shape of the data distribution (e.g., symmetric, skewed).
They are easy to construct by hand for smaller datasets.
Limitations:
They become cluttered and difficult to manage with very large datasets.
They are not practical for data with a very wide range or with many digits, as the stems can become too long.
8. Can stem-and-leaf plots be used for data with decimals or negative numbers?
Yes, stem-and-leaf plots are versatile enough to handle both decimals and negative numbers, but it requires a clear 'key'.
For Decimals: The stem can represent the whole number part and the leaf can represent the first decimal place. The key is essential, for example, Key: 5|2 = 5.2.
For Negative Numbers: The stems can be negative. The plot is arranged with stems becoming less negative (i.e., closer to zero) as you move down. For example, a stem of -2 and leaf of 1 would represent -21, while a stem of -0 and leaf of 5 could represent -5.
