Stem-and-Leaf Plot Examples: 44 Problems with Answers
Start with the recap, study the fully worked examples, then use the practice problems to
check your understanding of Stem-and-Leaf Plot.
This page combines explanation, solved examples, and follow-up practice so you can move
from recognition to confident problem-solving in Statistics.
Concept Recap
A stem-and-leaf plot displays numerical data by splitting each value into a stem and a leaf. It shows the distribution of the data while keeping the original values visible.
A stem-and-leaf plot is like a sorted list and a graph at the same time. You can see clusters, gaps, and repeated values without losing the exact numbers.
Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:Stem-and-Leaf Plot organizes data so the right pattern is visible without distorting the counts or scale.
Common stuck point:Students often know a procedure related to stem-and-leaf plot but skip the recognition step: Am I choosing or interpreting a display that matches the type of data and the question being asked? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint:Ask: Am I choosing or interpreting a display that matches the type of data and the question being asked?
Worked Examples
Example 1
medium
Build a stem-and-leaf plot for: 34,28,41,35,29,42,33,47 (key 2∣8=28). List the rows.Completed plot for: 34, 28, 41, 35, 29, 42, 33, 47.
Answer
2∣89;3∣345;4∣127
First step
1
Sort the data: 28,29,33,34,35,41,42,47.
See the full worked solution + why-it-works coaching
Setup·Key insight·Why it works·Common pitfall·Connection
Plot: 1∣2448; 2∣137; 3∣05 (key 1∣2=12). Find the mean.Find the mean of these 9 values.
Example 3
hard
Plot: 1∣258; 2∣0137; 3∣4 (key 1∣2=12). Find the IQR.Find the IQR (Q3 − Q1).
Example 4
hard
Test scores: 72,85,91,68,77,85,79,88,92,73,80,85. Build a stem-and-leaf plot (key 6∣8=68).Completed stem-and-leaf plot for the 12 test scores.
Example 5
hard
A back-to-back stem-and-leaf for two classes shows that Class A leaves are mostly on stem 7–8 while Class B's are spread across stems 5–9. What does this say about the two distributions?
Example 6
challenge
A stem-and-leaf plot of 20 exam scores shows: 5∣79; 6∣12489; 7∣035568; 8∣12459; 9∣05 (key 5∣7=57). Find the median, the mean, and identify any outliers using the 1.5×IQR rule.Find the median, mean, and check for outliers.
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
A stem-and-leaf plot has stem 3 with leaves 1, 4, 7 (key: 3|1 = 31). List the data values for stem 3.What are the data values for stem 3?
Example 2
easy
A stem-and-leaf plot row reads 5 | 2 3 3 8 (key 5|2 = 52). How many values are in this row?How many values are in this row?
Example 3
easy
A stem-and-leaf plot has stems 1, 2, 3 with 4, 6, and 2 leaves respectively. How many data values total?
Example 4
easy
A stem-and-leaf plot's smallest value is in stem 2 with leaf 1 (key 2|1 = 21) and largest in stem 6 with leaf 5. What is the range?Find the range: max minus min.
Example 5
easy
A stem-and-leaf plot has stem 4 with leaves 2 2 2 5 (key 4|2 = 42). Which value appears most often in this row?
Example 6
easy
A stem-and-leaf plot keeps original values visible. Stem 7 has leaves 0 4 (key 7|0 = 70). What are the exact values?What are the exact values shown?
Example 7
easy
Is a stem-and-leaf plot best for (A) two-digit test scores of 20 students, or (B) the favorite colors of a class?
Example 8
easy
A stem-and-leaf plot row is 8 | 1 3 9 (key 8|1 = 81). What is the largest value in this row?
Example 9
medium
A stem-and-leaf plot: 1|2 5; 2|0 3 8; 3|1 (key 1|2 = 12). Find the median of all values.Find the median of all six values.
Example 10
medium
A stem-and-leaf plot: 4|1 1 6; 5|2 9; 6|0 (key 4|1 = 41). What is the mean of all values?Find the mean of all values.
Example 11
medium
A stem-and-leaf plot: 2|3 7; 3|1 1 4 8; 4|2 (key 2|3 = 23). What is the mode?
Example 12
medium
A stem-and-leaf plot has 12 values. Stems 1,2,3 hold 5, 4, 3 leaves. The 7th value when ordered is 24. Which stem contains the median position values for an even count, and what is needed to find the median?
Example 13
medium
A stem-and-leaf plot: 5|0 4; 6|1 3 7; 7|2 8 (key 5|0 = 50). Find Q1 (the median of the lower half).Find Q1 (median of the lower half).
Example 14
medium
A stem-and-leaf plot row for stem 9 reads 9 | 0 0 5 (key 9|0 = 90). What fraction of a 10-value dataset is in the 90s?What fraction of the dataset is in the 90s?
Example 15
medium
A back-to-back stem-and-leaf plot compares two classes on stem 7. Class A leaves: 2 5 8; Class B leaves: 0 3. How many more students scored in the 70s in Class A than Class B?
Example 16
medium
A stem-and-leaf plot: 1|5; 2|0 4 4; 3|1 6; 4|9 (key 1|5 = 15). What is the range, and is 49 an outlier by the 'far from the rest' eye test?Find the range. Is 49 an outlier?
Example 17
medium
A stem-and-leaf plot: 3|2 8; 4|0 5 5 9; 5|1 (key 3|2 = 32). What value is at the 4th position when ordered?What value is at the 4th position when ordered?
Example 18
challenge
A stem-and-leaf plot has stems 2, 3, 4 with the same number of leaves each, totaling 9 values, and a median of 35. The stem-3 leaves are 1, 5, 9. What is the median, and which value is it?
Example 19
challenge
A stem-and-leaf plot of 8 values has IQR 20. The values are 2|2 5; 3|0 8; 4|1 7; 5|3 6 (key 2|2 = 22). Verify the IQR.Verify the IQR (Q3 − Q1).
Example 20
challenge
A stem-and-leaf plot of 10 quiz scores (out of 100) has stems 6,7,8,9. Stem 8 holds leaves 0 0 5 5 5. If the overall mean is 79, what is the sum of the values NOT in the 80s?
Example 21
easy
A stem-and-leaf plot row reads 6∣0259 (key 6∣0=60). List the data values in this row.List the data values in this row.
Example 22
easy
A stem-and-leaf plot row is 9∣115 (key 9∣1=91). How many values are in this row?How many values are in this row?
Example 23
easy
A stem-and-leaf plot has stems 0,1,2 with 3,5,2 leaves respectively. How many values in total?
Example 24
easy
What is the smallest value in this plot? 1∣49; 2∣25; 3∣0 (key 1∣4=14).What is the smallest value in this plot?
Example 25
easy
What is the largest value in this plot? 4∣26; 5∣138; 6∣0 (key 4∣2=42).What is the largest value in this plot?
Example 26
medium
Plot: 1∣05; 2∣249; 3∣18 (key 1∣0=10). What is the range?Find the range (max − min).
Example 27
medium
Plot: 3∣27; 4∣1448; 5∣0 (key 3∣2=32). What is the median?
Example 28
medium
Plot: 2∣136; 3∣25; 4∣07 (key 2∣1=21). What is the mode?What is the mode? (Check for repeated leaves.)
Example 29
medium
Plot: 5∣258; 6∣0337; 7∣1 (key 5∣2=52). How many values are at least 63?How many values are at least 63?
Example 30
medium
Plot: 0∣37; 1∣225; 2∣4 (key 0∣3=3). What is the median?
Example 31
medium
A back-to-back stem-and-leaf plot compares two groups. Group A leaves are read right-to-left from the stem, group B left-to-right. Why is this layout useful?
Example 32
hard
Plot: 4∣13; 5∣0588; 6∣27; 7∣1 (key 4∣1=41). Find Q1 and Q3.Find Q1 and Q3.
Example 33
hard
In the plot 2∣38; 3∣159; 4∣2677; 5∣0 (key 2∣3=23), what percent of values are at least 40?What percent of values are at least 40?
Example 34
hard
A truncated stem-and-leaf plot uses stem 12 with leaves 3,5,8 where the key reads 12∣3=123. List the values.
Example 35
hard
Plot: 0∣5; 1∣039; 2∣2 (key 0∣5=0.5, decimals). What is the mean?Find the mean (decimal scale: key 0|5
Example 36
hard
Plot: 2∣5; 3∣14; 4∣0268; 5∣17; 6∣3 (key 2∣5=25). Describe the shape.Describe the shape of this distribution.
Example 37
medium
Plot: 1∣1; 2∣47; 3∣2558; 4∣16 (key 1∣1=11). What is the mode?
Example 38
challenge
A stem-and-leaf plot has 25 values with median 46 and IQR 14. A new value 90 is added, making 26 values. Which summary statistic is most affected: median, IQR, or mean?