Statistics
Grade 3-4Stem and Leaf Diagrams
A stem and leaf diagram sorts data into place-value groups while keeping every original value visible, which makes it easy to find the mode, median and range directly from the diagram. This lesson covers reading values from a stem and leaf diagram, finding the mode, median and range, and comparing two data sets using a back-to-back stem and leaf diagram.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Reading values from a stem and leaf diagram
Each stem represents the leading digit or digits of a value, and each leaf represents the final digit. Combine a stem with one of its leaves to read off a full value, using the key to check the correct place value.
With the key "2 | 3 means 23", a stem of 2 and a leaf of 3 combine to give the value 23.
Finding the mode and median
The mode is the value that appears most often, which shows up as a repeated leaf within the same stem. The median is the middle value once the data is in order, which a stem and leaf diagram already provides, so just count along to find the middle position.
In a diagram with 9 values, the median is the 5th value once every stem and leaf combination is listed in order from smallest to largest.
Finding the range
The smallest value is found from the lowest stem's smallest leaf, and the largest value is found from the highest stem's largest leaf. Subtract the smallest from the largest to find the range.
If the smallest value in a diagram is 13 and the largest is 39, the range is 39 − 13 = 26.
Comparing data sets with a back-to-back stem and leaf diagram
A back-to-back diagram shares one stem column between two data sets, with leaves for one set on the left and leaves for the other on the right. Read the left-hand leaves in the same order they are printed to build the left data set's values, then compare statistics such as the median between the two sides.
With 9 values on each side of a back-to-back diagram, the median for each data set is its own 5th value, and these can be compared directly to see which data set is higher or more consistent.
Worked Examples
Three exam-style questions, fully solved.
The stem-and-leaf diagram shows the ages of 12 people at a club, with stems 1, 2 and 3. Stem 2 has leaves 0, 2, 3, 6, 7. How many people are in their twenties (20-29)?
Easy- 1.Count the number of leaves on the stem 2 row: 0, 2, 3, 6, 7
Answer: 5 people
The stem-and-leaf diagram shows the ages of 9 people at a club: stem 1 has leaves 2, 5, 9; stem 2 has leaves 1, 3, 4, 6, 8; stem 3 has leaf 0. Find the median age.
Medium- 1.Count the total number of values: 3 + 5 + 1 = 9
- 2.Find the middle position: the 5th value
- 3.Count through the ordered values (12, 15, 19, 21, 23, 24, 26, 28, 30) to the 5th one
Answer: 23
A back-to-back stem-and-leaf diagram shows the test scores of Class A and Class B (9 students each), sharing stems 5, 6, 7 and 8. Compare the median scores of the two classes.
Hard- 1.Order Class A's 9 values and find the 5th: median = 69
- 2.Order Class B's 9 values and find the 5th: median = 72
- 3.Compare the two medians: 72 is greater than 69
Answer: Class B has the higher median score
Avoid These
The most common mistakes students make.
Misreading how the stem and leaf combine to form a value, without checking the key, especially when the stem represents tens versus a different place value.
Assuming the leaves need to be reordered when finding the median, when a properly drawn stem and leaf diagram already lists leaves in ascending order within each stem.
Miscounting the middle position when finding the median, especially in a data set with an even number of values, where the median is the mean of the two middle values.
In a back-to-back stem and leaf diagram, mixing up which side belongs to which data set when comparing statistics.
When finding the range, using the smallest and largest leaf from the same stem instead of the true smallest and largest values across the whole diagram.
FAQ
Questions parents and students ask.
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