Stem –and–Leaf Plots

Stem and leaf plots get represented in the form of a special kind of table where each \(1\)^st digit or numeral of data value gets split up into a stem and then the final digit of information in a leaf. This ” \(|\) ” symbol is utilized to exhibit stem and leaf values and it’s known as the stem and leaf plot key.

Related Topics

• Pie Graphs
• Bar Graph
• Line Graphs
• Pictographs and Tally Charts

How do you Read Stem and Leaf Plots?

A stem and leaf plot key assists in understanding the data values. The stem is shown on the left but a leaf is shown on the right. If the values of the stem and the leaves are combined, you end up with the data values.

How do you Split a Stem and Leaf Plot?

A split stem and leaf plot divides each stem into numerous stems dependent on its occurrence. We put smaller leaves on the \(1\)st part of a split stem and put the bigger leaves on successive stems.

How do you create a Stem and Leaf Plot?

Follow these steps to create a stem and leaf plot.

• Step one: Examine the info and locate the number of figures. Categorize them as two or three-digit numerals.
• Step two: Install a stem and leaf plot key. For instance, \(2\) | \(4 = 24\), as well as \(3\) | \(1\) is \(31\).
• Step three: Distinguish the \(1\)st figures as stems and make the final numeral as leaves.
• Step four: Define the data’s range, i.e. the bottom and the top values amongst your data.
• Step five: Create a vertical line. Put the stem on the lefthand column and put the leaf on the righthand column.
• Step 6: Put these stems in the stems column. Organize it in rising order beginning with the lowest possible to the highest.
• Step seven: Plot these leaves in the column compared to the stem from the least to the most horizontally.

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Crucial Notes

Here are a few vital notes related to stem and leaf plots. Be sure to read them!

• If info is plotted using stem and leaf and you place the data next to the brand-new information, we may be able to notice a link between both the data and the frequency of dissemination of information.
• A stem and leaf plot key for \(3\)-digit numbers is characterized via \(2\) digits in a stem as well as \(1\) numeral in a leaf. For instance, \(43\) | \(2\) \(= 432\)
• The mean, mode, and median of the provided info are calculated easily by utilizing stem and leaf plots.

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Stem –and–Leaf Plots – Example 1:

Make a stem and leaf plot for the given data.

\(42,35,13,22,17,33,25\)

Solution:

First, you should arrange data from small to large: \(13,17,22,25,33,35,42\). Draw a stem-and-leaf plot. Note that the stem is the left column and the leaf is the right column. Divide each number into two parts: stem part and leaf part. The “ones’” digit is located in the leaf column. Note if the data is in one digit, we put zero in the stem section.

Stem –and–Leaf Plots – Example 2:

Make a stem and leaf plot for the given data.

\(110,121,135,115,122,136\)

Solution:

First, you should arrange data from small to large: \(110,115,121,122,135,136\). Draw a stem-and-leaf plot. Note that the stem is the left column and the leaf is the right column. Divide each number into two parts: stem part and leaf part. The “ones’” digit is located in the leaf column. Note if the data is in one digit, we put zero in the stem section.

Exercises for Stem –and–Leaf Plots

Make stem and leaf plots for the given data.

1. \(\color{blue}{54,76,62,56,71,60,45}\)
2. \(\color{blue}{170,166,193,182,163,171,195,174}\)

1.

2.

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Frequently Asked Questions

What is a stem-and-leaf plot?

A simple data display that splits each number into a stem (leading digits) and a leaf (the last digit). Stems run down the left column; leaves attach to their stems on the right. It is a quick way to display data while preserving every value.

Give a quick example.

For data 23, 25, 26, 31, 31, 34, 42, 47: stem 2 has leaves 3, 5, 6; stem 3 has leaves 1, 1, 4; stem 4 has leaves 2, 7. Reading across, you can reconstruct every original value.

How do I find the median from a stem-and-leaf plot?

Count the total number of leaves to find the middle position(s). Then count from the smallest value (top-left) until you reach that position — that value is the median.

How do I find the mode?

Look for repeated leaves on the same stem — those are repeated values. The mode is the value (or values) appearing most often. If a stem has two of the same leaf, that value appears twice.

How do I find the range?

Range = maximum minus minimum. The maximum is the largest value (largest stem, largest leaf on that stem). The minimum is the smallest value (smallest stem, smallest leaf on that stem).

What is a back-to-back stem-and-leaf plot?

A way to compare two data sets. The stems sit in the middle, with one data set’s leaves extending to the left and the other to the right. Useful for side-by-side distributions.

How does a stem-and-leaf plot compare to a histogram?

A histogram shows the shape of the distribution but loses individual values. A stem-and-leaf plot shows the shape AND preserves every original value. The trade-off: stem-and-leaf gets unwieldy for large data sets, while histograms scale easily.

Can I use decimal data in a stem-and-leaf plot?

Yes. For data like 5.2, 5.7, 6.1, 6.4: the stem is the whole number and the leaf is the tenths digit. Stem 5 has leaves 2, 7; stem 6 has leaves 1, 4. Always note the decimal convention in a key.

When is a stem-and-leaf plot the right choice?

For small-to-medium data sets (about 10-50 values) where you want both the shape AND individual values visible. For larger data sets, switch to a histogram or box plot.

What grade level introduces stem-and-leaf plots?

Most curricula introduce them in Grade 5 or 6 as part of data display. They appear on state tests through middle school and as a basic tool in introductory statistics.

Related Lessons You May Like

• How to find the measures of central tendency
• How to find range, quartile, and interquartile range
• How to graph a box plot
• How to interpret a histogram
• How to read a frequency distribution table

For a friendly tour of statistics that builds intuition first, Pre-Algebra for Beginners covers the basics. For deeper work, Algebra II for Beginners moves into inferential statistics.