Solve the Puzzle of Stem and Leaf Plots

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Have you ever encountered a stem and leaf plot and wondered what it is and how to interpret it? If so, you're not alone. While stem and leaf plots may seem confusing initially, they are a simple and effective way to visualize data and understand its distribution. So if you're ready to solve the puzzle of stem and leaf plots, read on! In this blog, we will take a deep dive into stem and leaf plots, explaining what they are, how to create them, and how to use them to gain valuable insights into your data.

What is a Stem and Leaf Plot?

A stem and leaf plot is a graphical tool used to display and organize data to allow easy interpretation of its distribution. It is similar to a histogram, but instead of showing the frequency of data within specified bins, a stem and leaf plot displays each individual data point.

The plot is constructed by dividing each data point into two parts: the stem, which represents the tens digit, and the leaf, which represents the ones digit. For example, 35 would be divided into a stem of 3 and a leaf of 5. These stem and leaf pairs are then organized and plotted on a chart, with the stems on the left and the leaves on the right.

Stem and leaf plots are useful for displaying small to medium-sized datasets and can help identify patterns and trends in the data.  They are often used in statistics and data analysis but can also be helpful for anyone looking to gain a better understanding of their data. Minitab suggests using this plot when you have a number of data points less than 50.

Understanding Stem and Leaf Plot

There is no direct method to draw a stem and leaf plot in Microsoft Excel.

You can quickly draw it in Minitab and other statistical software. Let's try to understand a stem and leaf plot created in Minitab.

In the above snapshot, we have 17 raw values listed in the left corner, the descriptive statistics of these values at the top, and in the middle, we have the stem and leaf plot. Let's try to interpret the plot.

The Second Column of Stem Plot:

The second column is the stem. In this case, it is the tens in the number. For example, data point 38 will have 3 as the stem and 8 as the leaf.

The Third Column of Stem Plot:

The third column of the stem and leaf plot is the "leaf." For example, the leaf value for data point 38 is 8.

Based on our understanding of the 2nd and 3rd columns, if I read the 4th row (6  |  4  | 059), it tells me that the data contains three values starting with 4, which are 40, 45 and 49.

The First Column of Stem Plot:

The first column of the stem plot counts the number of values from the top down and the bottom up to the middle value. For example, the second number in the first column is 6. It means there are 6 items with the first number starting with 1 or 2.

Similarly, the number 3 in the first column shows that there are three items with the first number as 5, 6 or 7.

The row containing the median is shown in parentheses (5), and the number in the parentheses is the total number of items in this row.

This column helps us in finding out the median. In this case, we can see that the number of values above and below the row containing the median are 6. That means the median will be the middle value in the third row, and the third row contains 5 values. Based on this, we can conclude that the median here is 37.

Plotting a Stem and Leaf Plot

To create a stem and leaf plot, the data set is first divided into two parts: the stem and the leaf. The stem represents the leading digit(s) of each value in the data set, and the leaf represents the remaining digits of each value. For example, if the data set contains the values 12, 15, 21, 23, 27, and 32, the stem would be the leading digit (1, 2 or 3) of each value, and the leaf would be the remaining digits (2, 5, 1, 3, 7, and 2) of each value.

The stem and leaf plot, in this case, will look something like this:

1 | 25

2 | 137

3 | 2


Conclusion:

Stem and leaf plots help show the shape of data distribution and identify patterns or trends within the data. They can also be used to compare the distributions of multiple data sets and to identify potential outliers in the data.


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