Lesson 7 ~25 min Unit 4 · Data & Chance +85 XP

Stem-and-Leaf Plots and Dot Plots

Display every data value while revealing the shape, clusters and outliers of your data set.

Today's hook: What if you could see every single data value AND the shape of the data at the same time? That's exactly what a stem-and-leaf plot does — it's the Swiss Army knife of data displays.

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Think First

warm-up

Before you read on — here are 10 test scores: 34, 41, 28, 52, 37, 41, 29, 33, 45, 55. How would you organise these to make them easy to analyse? Is there a pattern? Try it, then check your reasoning as you go.

Record your answer in your workbook.

The Big Idea

+5 XP

A stem-and-leaf plot displays all data values while also showing the shape of the distribution. The stem is the leading digit(s) (usually tens); the leaf is the last digit (units). A dot plot shows each value as a dot above a number line — great for small data sets.

For the data 34, 28, 37, 29, 33: stems are 2 and 3. Leaves for stem 2: 8, 9; for stem 3: 3, 4, 7. Read "2 | 8" as 28 and "3 | 4" as 34. Leaves must always be in ascending order so you can read the median directly.

Stem = tens digit | Leaf = units digit | Always sort leaves

Stem = leading digits

For 2-digit data: stem = tens. For 3-digit: stem = hundreds and tens.

Sort leaves smallest first

Always write leaves in ascending order across each stem row.

Include a key

Always write "Key: 2 | 8 = 28" so readers know how to interpret the plot.

What You'll Master

objectives

Know

What stems and leaves are and which digit each represents
How to write a key for a stem-and-leaf plot
What a dot plot is and when to use it

Understand

Why leaves must always be in ascending order
How the plot shape reveals the data distribution
What clusters, gaps and outliers look like visually

Can Do

Construct a stem-and-leaf plot from raw data
Read the median and mode from a completed plot
Draw a dot plot and describe its shape, clusters and outliers

Words You Need

vocabulary

StemThe leading digit(s) of each value in a stem-and-leaf plot (usually the tens digit).

LeafThe last digit of each value in a stem-and-leaf plot (always the units digit).

DistributionThe overall pattern of how data values are spread across their range.

ClusterA group of data values that are close together, forming a dense region in the display.

GapAn interval with no data values, creating a break between regions of the data.

OutlierA value that sits far above or below the main group of data — it looks isolated.

Spot the Trap

heads-up

Wrong: Writing leaves unsorted — e.g. "3 | 7 4 1" instead of "3 | 1 4 7". Unsorted leaves hide the distribution shape and make it impossible to read the median.

Right: Do a rough draft first, then rewrite with leaves sorted from smallest to largest in each row: "3 | 1 4 7".

Wrong: Reading "3 | 5" as 53 (leaf first). The stem is on the left, so "3 | 5" always means 35, not 53.

Right: Stem first (tens), leaf second (units). Check your key: "Key: 3 | 5 = 35" confirms this every time.

Drawing a Stem-and-Leaf Plot

+5 XP

Four steps to build a stem-and-leaf plot: (1) find the range and list all stems in order. (2) Write each leaf next to its stem (unsorted draft). (3) Rewrite with leaves in ascending order. (4) Write a key.

Data: 23, 31, 45, 28, 37, 42, 23, 51. Stems: 2, 3, 4, 5. Draft: 2|3 8 3, 3|1 7, 4|5 2, 5|1. Sorted: 2|3 3 8, 3|1 7, 4|2 5, 5|1. Key: 2|3 = 23. The longest row (stem 2) shows where most data clusters.

List stems → Draft leaves → Sort leaves → Write key

Include empty stems

If no data falls in a stem row, still include it with no leaves (e.g. "6 |").

Draft then sort

Write unsorted leaves first, then rewrite neatly with leaves in order.

Count to verify

Count all leaves — the total must equal n (the number of data values).

Reading from a Stem-and-Leaf Plot

+5 XP

Once the plot is complete with sorted leaves, you can read off the median (middle value), mode (most common value), and range (max − min) directly without resorting.

From the ordered plot above (n = 8): Min = 23, Max = 51, Range = 28. For the median of 8 values: the middle is between the 4th and 5th. Count the leaves in order: 23, 23, 28, 31, 37, 42, 45, 51. Median = (31+37)÷2 = 34. Mode = 23 (the only repeated value).

Median = middle leaf | Mode = repeated value | Range = max − min

Count ALL leaves

Add up leaves across every row to get n, then find the middle position(s).

Mode = repeated leaf

Look for a leaf that appears more than once in its row. The mode is stem + that leaf.

Min and max are easy

Min = top row's first leaf + stem. Max = bottom row's last leaf + stem.

Dot Plots

+5 XP

A dot plot places one dot above a number line for each data value. When values repeat, dots stack vertically. Dot plots reveal clusters (bunches of dots), gaps (empty spaces) and outliers (isolated dots). They work best for small data sets.

Data: 3, 5, 3, 7, 5, 3, 8. Number line from 2 to 9. Value 3 appears 3 times → 3 stacked dots above 3. Value 5 appears twice → 2 stacked dots. Values 7 and 8 get one dot each. Description: "Cluster at 3 and 5. Gap at 6. Value 8 is a mild outlier."

One dot per value → Stack repeats → Describe clusters, gaps, outliers

One dot per data value

If 3 appears five times, draw 5 separate stacked dots — never one big dot.

Name what you see

Always describe clusters, gaps and any outliers when interpreting a dot plot.

Label the axis

Write the variable name under the number line (e.g. "Score out of 10").

Watch Me Solve It · 3 examples

Watch Me Solve It · Build a stem-and-leaf plot

+15 XP per step

PROBLEM

Build an ordered stem-and-leaf plot for: 34, 41, 28, 52, 37, 41, 29, 33, 45, 55.

1

Identify the stems

Data range: 28 to 55. Stems needed: 2, 3, 4, 5

Each stem represents the tens digit. List them vertically from smallest to largest.
2

Draft the leaves (unsorted)

2|8 9 3|4 7 3 4|1 1 5 5|2 5

Write the units digit of each value next to its stem, in the order you encounter the data.
3

Sort leaves and write key

2|8 9 3|3 4 7 4|1 1 5 5|2 5 Key: 3|4 = 34

Sort each row ascending. Count: 2+3+3+2 = 10 leaves. Matches n = 10. Correct.

Answer2|8 9 3|3 4 7 4|1 1 5 5|2 5 Key: 3|4 = 34

Watch Me Solve It · Find median and mode from a plot

+15 XP per step

PROBLEM

From the ordered plot above (n=10): find the median and mode.

1

List all values from the plot in order

28, 29, 33, 34, 37, 41, 41, 45, 52, 55

Read across each row top to bottom — leaves are already sorted, so the full list is automatically in order.
2

Find the median (n = 10, even number)

5th value = 37, 6th value = 41. Median = (37 + 41) ÷ 2 = 39
3

Find the mode

Row 4|: leaves are 1, 1, 5. Leaf 1 appears twice → value 41 is the only repeated value. Mode = 41

Check every row for repeated leaves. Only stem 4, leaf 1 repeats here — giving mode = 41.

AnswerMedian = 39. Mode = 41.

Watch Me Solve It · Draw and describe a dot plot

+15 XP per step

PROBLEM

Draw a dot plot for: 3, 5, 3, 7, 5, 3, 8. Describe its shape.

1

Draw the number line

Draw a horizontal axis labelled "Data value" spanning from 2 to 9.

Span from just below the minimum (3) to just above the maximum (8) to display all values clearly.
2

Place one dot per data value

Above 3: 3 stacked dots. Above 5: 2 stacked dots. Above 7: 1 dot. Above 8: 1 dot.
3

Describe the distribution

"Cluster at 3 and 5. Gap at 4 and 6. The value 8 is a mild outlier, sitting apart from the main group."

Most data is in the lower range (3–5). Values 7 and 8 are isolated from this cluster.

Answer3 dots at 3, 2 dots at 5, 1 dot at 7, 1 dot at 8. Cluster at 3–5; gap at 4 and 6; mild outlier at 8.

Common Pitfalls

heads-up

Leaves not in order

Writing leaves as "3 | 7 4 1" hides the distribution shape and makes finding the median impossible without resorting. Every mark scheme checks that leaves are ordered.

Fix: Always do an unsorted rough draft first, then rewrite with leaves sorted smallest to largest in each row.

Missing a data value

If your leaf count doesn't equal n, you've left out a value. Every missing leaf changes the median, mode and range you calculate from the plot.

Fix: After completing the plot, count every leaf. Total must equal n. Go back and find the missing value if they don't match.

Reading the stem and leaf backwards

Students sometimes read "3 | 5" as 53 instead of 35, thinking the leaf comes first. But the stem (left side) always gives the tens digit, and the leaf gives the units.

Fix: Always write and check your key. "Key: 3 | 5 = 35" — if it reads 35, you're doing it right.

Copy Into Your Books

Stem-and-Leaf: Structure

Stem = tens digit (left of the line)
Leaf = units digit (right of the line)
3|7 means 37 — always stem first
Include a key: "Key: 3|7 = 37"

Building the Plot

List all stems (include empty rows)
Draft leaves unsorted first
Rewrite with leaves in ascending order
Count leaves = n to verify

Reading Statistics

Median: count to the middle leaf position
Mode: look for a repeated leaf in a row
Range: max − min (top and bottom values)

Dot Plots

One dot per value above a number line
Stack dots for repeated values
Cluster = bunched dots; Gap = no dots; Outlier = isolated dot
Label the number line axis

How are you completing this lesson?

Brain Trainer · 4 problems

Brain Trainer · Stem-and-Leaf and Dot Plots

4 problems

Four drill problems to sharpen your skills. Work each, then reveal the answer.

1 Build a stem-and-leaf plot for: 34, 41, 28, 52, 37, 41, 29, 33, 45, 55.

2|8 9 3|3 4 7 4|1 1 5 5|2 5 Key: 3|4 = 34 (10 leaves ✓)
2 What is the median of the data above? (n = 10)

Ordered: 28,29,33,34,37,41,41,45,52,55. 5th=37, 6th=41. Median = (37+41)÷2 = 39
3 How many values from the data above are in the 40s?

Stem 4 has leaves 1, 1, 5 → values 41, 41, 45. 3 values in the 40s
4 Draw a dot plot for: 3, 5, 3, 7, 5, 3, 8. How many dots are above the value 3?

The value 3 appears three times. Each occurrence gets its own dot, stacked vertically. 3 dots above the value 3

Complete in your workbook.

Quick Check · 5 questions

In a stem-and-leaf plot, what does 4 | 7 represent?

+10 XP

How must leaves be arranged in each row of a stem-and-leaf plot?

+10 XP

What is an outlier on a dot plot?

+10 XP

What is the key advantage of a stem-and-leaf plot over a histogram?

+10 XP

On a dot plot, what does a cluster show?

+10 XP

Show Your Working · 3 questions

Show Your Working

9 marks total

Apply Medium 4 MARKS

Q6. Construct a stem-and-leaf plot for the following heights (cm): 142, 156, 138, 165, 149, 152, 138, 161, 147, 155. Find the range and median from your plot.

Answer in your workbook.

Understand Easy 2 MARKS

Q7. A stem-and-leaf plot shows: 2|3 5 5 8, 3|1 4 6, 4|2. How many data values are in the 20s, and what is the mode?

Answer in your workbook.

Evaluate Hard 3 MARKS

Q8. A dot plot shows scores: two dots at 5, four dots at 6, one dot at 7, one dot at 12. Identify clusters, gaps and any outlier. Explain how the outlier affects your description of a typical score.

Answer in your workbook.

Comprehensive Answers

Quick Check

1. C — 4|7 = 47. Stem (tens) + leaf (units).

2. B — Ascending order (smallest to largest) within each row.

3. D — An outlier is a value much higher or lower than the rest.

4. A — Stem-and-leaf plots preserve every individual data value.

5. B — A cluster is where many data values are concentrated.

Show Your Working Model Answers

Q6 (4 marks): 13|8 8 14|2 7 9 15|2 5 6 16|1 5 [2 marks for correct ordered plot]. Key: 13|8=138 [1]. Range = 165−138 = 27 cm. Median (n=10): 5th=149, 6th=152, median = (149+152)÷2 = 150.5 cm [1].

Q7 (2 marks): Values in 20s: stem 2 has leaves 3,5,5,8 → 4 values [1]. Mode = 25 (leaf 5 appears twice in stem 2; 25 is the only repeated value) [1].

Q8 (3 marks): Cluster at 5–6 (most data here) [1]. Gap at 8–11 [1]. Outlier at 12. The outlier pulls the mean upward and makes the range large (12−5=7), giving a misleading impression of a typical score of around 10+ when most scores are 5–7 [1].

Stretch Challenge · +25 XP, +10 coins

The Back-to-Back Plot

Class A test scores: 45, 52, 38, 61, 57, 43, 55, 49, 62, 38. Class B scores: 71, 63, 58, 75, 66, 80, 59, 68, 72, 64. Build a back-to-back stem-and-leaf plot with Class A on the left and Class B on the right. Then: (a) Which class had the higher median? (b) Which class had the greater range? (c) Which class performed more consistently? Justify using the plot.

Reveal solution

Back-to-back: 8 8 3|3| 9 3|4| 7 5 2|5|8 9 2 1|6|3 4 6 8 |7|1 2 5 |8|0. Class A median (n=10): 5th=49, 6th=52, med=50.5. Class B median: 5th=66, 6th=68, med=67. (a) Class B higher. Class A range=62−38=24. Class B range=80−58=22. (b) Class A has greater range. (c) Class B more consistent: smaller range and data concentrated in 60s–70s, while Class A is spread from 38 to 62.

Quick Review

Stem = tens, Leaf = units

3|7 = 37. Always stem first, leaf second. Include a key every time.

Sort leaves ascending

Draft unsorted first, then rewrite in order. Count leaves = n to verify.

Median from the plot

Count all leaves; find the middle position(s). Average two middles if n is even.

Mode = repeated leaf

Look for a leaf that appears more than once in a row; mode = stem + that leaf.

Dot plots: one dot per value

Stack dots for repeats. Label the axis. Describe clusters, gaps and outliers.

Clusters vs gaps vs outliers

Cluster = bunched dots. Gap = no dots in a region. Outlier = isolated far dot.

Interactive: Stem-and-Leaf Builder

Type in numbers and watch the stem-and-leaf plot build itself, then read off the statistics.

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