How to Make a Stem and Leaf Plot
Read,3 minutes
A stem-and-leaf plot keeps the original data values while organizing them like a graph. For two-digit numbers, the tens digit is usually the stem and the ones digit is the leaf.
How to Build One
- Order the data from least to greatest.
- Split each value into a stem and a leaf.
- Write leaves in increasing order beside each stem.
- Include a key, such as \(6\mid 4=64\), so the scale is clear.
Worked Example
The data \(42, 45, 51, 53, 53, 60\) become \(4\mid 2\ 5\), \(5\mid 1\ 3\ 3\), and \(6\mid 0\). The key is \(4\mid 2=42\).
Stem And Leaf Plot
Think of this lesson as more than a rule to memorize. Stem And Leaf Plot is about organizing data and choosing the right summary measure. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.
Statistics is about describing data clearly. First organize the values, then choose the measure or graph that best answers the question being asked.
Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.
- Read the scale and labels first.
- Identify the key values the graph shows.
- Connect the graph to the formula or data table.
- Answer using the units and context.
A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.
Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.
When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.
On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.
Exercises
Solve each ACT-style practice problem. The questions increase in difficulty.
1) Make a stem-and-leaf plot for \( 21, 24, 25, 28, 31, 33 \). Then find the median and range.
2) Make a stem-and-leaf plot for \( 12, 14, 18, 19, 22, 27, 29 \). Then find the median and range.
3) Make a stem-and-leaf plot for \( 35, 35, 38, 41, 44, 46, 49 \). Then find the median and range.
4) Make a stem-and-leaf plot for \( 50, 52, 55, 57, 60, 63, 66, 69 \). Then find the median and range.
5) Make a stem-and-leaf plot for \( 7, 9, 11, 13, 15, 17, 19, 21 \). Then find the median and range.
6) Make a stem-and-leaf plot for \( 42, 45, 45, 48, 51, 54, 57, 59 \). Then find the median and range.
7) Make a stem-and-leaf plot for \( 61, 63, 65, 65, 68, 70, 72, 75 \). Then find the median and range.
8) Make a stem-and-leaf plot for \( 28, 31, 34, 36, 39, 42, 45, 48, 51 \). Then find the median and range.
9) Make a stem-and-leaf plot for \( 15, 18, 22, 22, 24, 27, 31, 35, 39 \). Then find the median and range.
10) Make a stem-and-leaf plot for \( 73, 75, 78, 80, 82, 85, 88, 91, 94 \). Then find the median and range.
11) Make a stem-and-leaf plot for \( 101, 104, 109, 112, 115, 118, 121, 124 \). Then find the median and range.
12) Make a stem-and-leaf plot for \( 33, 37, 37, 40, 44, 49, 52, 56, 60, 65 \). Then find the median and range.
13) Make a stem-and-leaf plot for \( 18, 21, 25, 29, 34, 34, 38, 42, 47, 53 \). Then find the median and range.
14) Make a stem-and-leaf plot for \( 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 \). Then find the median and range.
15) Make a stem-and-leaf plot for \( 82, 84, 84, 86, 89, 91, 95, 97, 99, 100 \). Then find the median and range.
16) Make a stem-and-leaf plot for \( 45, 49, 52, 58, 61, 67, 70, 76, 83, 89, 92 \). Then find the median and range.
17) Make a stem-and-leaf plot for \( 14, 14, 19, 23, 28, 28, 32, 37, 41, 46, 50 \). Then find the median and range.
18) Make a stem-and-leaf plot for \( 105, 108, 111, 115, 119, 123, 128, 132, 137, 141 \). Then find the median and range.
19) Make a stem-and-leaf plot for \( 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100 \). Then find the median and range.
20) Make a stem-and-leaf plot for \( 19, 23, 28, 34, 41, 47, 53, 59, 66, 72, 79, 85 \). Then find the median and range.
1) Order the values: \( 21, 24, 25, 28, 31, 33 \).
Use tens digits as stems and ones digits as leaves:
\(2 \mid 1 4 5 8\)
\(3 \mid 1 3\)
Key: \(2 \mid 1=21\).
The median is \(\frac{53}{2}\). The range is \(33-21=12\).
2) Order the values: \( 12, 14, 18, 19, 22, 27, 29 \).
Use tens digits as stems and ones digits as leaves:
\(1 \mid 2 4 8 9\)
\(2 \mid 2 7 9\)
Key: \(1 \mid 2=12\).
The median is \(19\). The range is \(29-12=17\).
3) Order the values: \( 35, 35, 38, 41, 44, 46, 49 \).
Use tens digits as stems and ones digits as leaves:
\(3 \mid 5 5 8\)
\(4 \mid 1 4 6 9\)
Key: \(3 \mid 5=35\).
The median is \(41\). The range is \(49-35=14\).
4) Order the values: \( 50, 52, 55, 57, 60, 63, 66, 69 \).
Use tens digits as stems and ones digits as leaves:
\(5 \mid 0 2 5 7\)
\(6 \mid 0 3 6 9\)
Key: \(5 \mid 0=50\).
The median is \(\frac{117}{2}\). The range is \(69-50=19\).
5) Order the values: \( 7, 9, 11, 13, 15, 17, 19, 21 \).
Use tens digits as stems and ones digits as leaves:
\(0 \mid 7 9\)
\(1 \mid 1 3 5 7 9\)
\(2 \mid 1\)
Key: \(0 \mid 7=7\).
The median is \(14\). The range is \(21-7=14\).
6) Order the values: \( 42, 45, 45, 48, 51, 54, 57, 59 \).
Use tens digits as stems and ones digits as leaves:
\(4 \mid 2 5 5 8\)
\(5 \mid 1 4 7 9\)
Key: \(4 \mid 2=42\).
The median is \(\frac{99}{2}\). The range is \(59-42=17\).
7) Order the values: \( 61, 63, 65, 65, 68, 70, 72, 75 \).
Use tens digits as stems and ones digits as leaves:
\(6 \mid 1 3 5 5 8\)
\(7 \mid 0 2 5\)
Key: \(6 \mid 1=61\).
The median is \(\frac{133}{2}\). The range is \(75-61=14\).
8) Order the values: \( 28, 31, 34, 36, 39, 42, 45, 48, 51 \).
Use tens digits as stems and ones digits as leaves:
\(2 \mid 8\)
\(3 \mid 1 4 6 9\)
\(4 \mid 2 5 8\)
\(5 \mid 1\)
Key: \(2 \mid 8=28\).
The median is \(39\). The range is \(51-28=23\).
9) Order the values: \( 15, 18, 22, 22, 24, 27, 31, 35, 39 \).
Use tens digits as stems and ones digits as leaves:
\(1 \mid 5 8\)
\(2 \mid 2 2 4 7\)
\(3 \mid 1 5 9\)
Key: \(1 \mid 5=15\).
The median is \(24\). The range is \(39-15=24\).
10) Order the values: \( 73, 75, 78, 80, 82, 85, 88, 91, 94 \).
Use tens digits as stems and ones digits as leaves:
\(7 \mid 3 5 8\)
\(8 \mid 0 2 5 8\)
\(9 \mid 1 4\)
Key: \(7 \mid 3=73\).
The median is \(82\). The range is \(94-73=21\).
11) Order the values: \( 101, 104, 109, 112, 115, 118, 121, 124 \).
Use tens digits as stems and ones digits as leaves:
\(10 \mid 1 4 9\)
\(11 \mid 2 5 8\)
\(12 \mid 1 4\)
Key: \(10 \mid 1=101\).
The median is \(\frac{227}{2}\). The range is \(124-101=23\).
12) Order the values: \( 33, 37, 37, 40, 44, 49, 52, 56, 60, 65 \).
Use tens digits as stems and ones digits as leaves:
\(3 \mid 3 7 7\)
\(4 \mid 0 4 9\)
\(5 \mid 2 6\)
\(6 \mid 0 5\)
Key: \(3 \mid 3=33\).
The median is \(\frac{93}{2}\). The range is \(65-33=32\).
13) Order the values: \( 18, 21, 25, 29, 34, 34, 38, 42, 47, 53 \).
Use tens digits as stems and ones digits as leaves:
\(1 \mid 8\)
\(2 \mid 1 5 9\)
\(3 \mid 4 4 8\)
\(4 \mid 2 7\)
\(5 \mid 3\)
Key: \(1 \mid 8=18\).
The median is \(34\). The range is \(53-18=35\).
14) Order the values: \( 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 \).
Use tens digits as stems and ones digits as leaves:
\(0 \mid 6\)
\(1 \mid 2 8\)
\(2 \mid 4\)
\(3 \mid 0 6\)
\(4 \mid 2 8\)
\(5 \mid 4\)
\(6 \mid 0\)
Key: \(0 \mid 6=6\).
The median is \(33\). The range is \(60-6=54\).
15) Order the values: \( 82, 84, 84, 86, 89, 91, 95, 97, 99, 100 \).
Use tens digits as stems and ones digits as leaves:
\(8 \mid 2 4 4 6 9\)
\(9 \mid 1 5 7 9\)
\(10 \mid 0\)
Key: \(8 \mid 2=82\).
The median is \(90\). The range is \(100-82=18\).
16) Order the values: \( 45, 49, 52, 58, 61, 67, 70, 76, 83, 89, 92 \).
Use tens digits as stems and ones digits as leaves:
\(4 \mid 5 9\)
\(5 \mid 2 8\)
\(6 \mid 1 7\)
\(7 \mid 0 6\)
\(8 \mid 3 9\)
\(9 \mid 2\)
Key: \(4 \mid 5=45\).
The median is \(67\). The range is \(92-45=47\).
17) Order the values: \( 14, 14, 19, 23, 28, 28, 32, 37, 41, 46, 50 \).
Use tens digits as stems and ones digits as leaves:
\(1 \mid 4 4 9\)
\(2 \mid 3 8 8\)
\(3 \mid 2 7\)
\(4 \mid 1 6\)
\(5 \mid 0\)
Key: \(1 \mid 4=14\).
The median is \(28\). The range is \(50-14=36\).
18) Order the values: \( 105, 108, 111, 115, 119, 123, 128, 132, 137, 141 \).
Use tens digits as stems and ones digits as leaves:
\(10 \mid 5 8\)
\(11 \mid 1 5 9\)
\(12 \mid 3 8\)
\(13 \mid 2 7\)
\(14 \mid 1\)
Key: \(10 \mid 5=105\).
The median is \(121\). The range is \(141-105=36\).
19) Order the values: \( 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100 \).
Use tens digits as stems and ones digits as leaves:
\(5 \mid 6\)
\(6 \mid 0 4 8\)
\(7 \mid 2 6\)
\(8 \mid 0 4 8\)
\(9 \mid 2 6\)
\(10 \mid 0\)
Key: \(5 \mid 6=56\).
The median is \(78\). The range is \(100-56=44\).
20) Order the values: \( 19, 23, 28, 34, 41, 47, 53, 59, 66, 72, 79, 85 \).
Use tens digits as stems and ones digits as leaves:
\(1 \mid 9\)
\(2 \mid 3 8\)
\(3 \mid 4\)
\(4 \mid 1 7\)
\(5 \mid 3 9\)
\(6 \mid 6\)
\(7 \mid 2 9\)
\(8 \mid 5\)
Key: \(1 \mid 9=19\).
The median is \(50\). The range is \(85-19=66\).
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