Represent Data with Dot Plots and Histograms

Lesson 1 of 2: Represent Data with Plots

In this lesson:

• Build a dot plot that shows every data value
• Build a histogram that reveals a distribution's shape

Learning Objectives for This Unit

By the end of this unit, you should be able to:

1. Construct dot plots, histograms, and box plots
2. Choose the right plot for the data and question
3. Interpret patterns, outliers, and shape
4. Compare the strengths of each plot type
5. Use technology to build displays efficiently

Recall: Plotting a Value on the Number Line

• A number line orders values left to right
• Plot a value: 76 → a point at the tick labeled 76
• Equal spacing means equal distance between values

Can you place a single number on a number line?

Fifteen Heart Rates, One Picture

Ms. Johnson's class measured resting heart rates (beats per minute):

68, 72, 72, 74, 76, 76, 76, 78, 80, 80, 82, 84, 88, 90, 92

Can one picture show every value — and where the class clusters?

Place the Dots, Then Stack Repeats

Put each heart rate as a dot on a number line:

• 68 → one dot above 68
• 76 → one dot above 76
• 76 again → no room, so stack it on top

Two students share a value? Stack the dots. That's the whole trick.

What a Dot Plot Shows

One dot per value; stacked dots show how often a value repeats.

Build the Dot Plot Step by Step

For the fifteen heart rates:

1. Draw a number line from 65 to 95, ticks every 2
2. Place one dot above each value, aligned to its tick
3. Stack the three dots at 76

Line every dot up exactly — a drifting dot misreports the data.

Read Features from the Plot

• Cluster 72–82, mode at 76
• Gap at 86, high value at 92

Quick Check on the Heart Rates

Using the dot plot of the fifteen heart rates:

1. How many students have a heart rate of 80?
2. What is the median of the fifteen values?

Commit to both answers before advancing.

Your Turn: Build a Dot Plot

Family reunion ages: 8, 10, 10, 12, 35, 38, 40, 42, 70

1. Draw and label a number line
2. Place and stack the dots
3. Name one cluster and one gap

Build the whole plot, then describe what you see.

When the Dots Become a Smear

The dot plot showed all 15 heart rates clearly.

Now imagine 600 heart rates on the same line:

• Stacks tower off the slide
• Dots blur into a solid smear

Too many values to show one at a time. We need to group them.

A Histogram Groups Values into Bins

A histogram sorts values into equal-width intervals called bins.

• One bar per bin, not one dot per value
• Bar height = how many values land in that bin

You give up individual values to gain a clear view of the shape.

Tally Black Friday Spending into Bins

Sixty customers' spending, grouped into $20 bins:

The bin [50, 70) includes $50 but stops just short of $70.

Draw the Histogram Bars That Touch

Bar height = bin count, and the bars touch — no gaps.

Why the Histogram Bars Must Touch

The bins are adjacent intervals on one continuous number line.

• The bin ending at $60 and the next beginning at $60 share that edge
• No spending value falls "between" two bins

Touching bars show continuity — a gap would claim a value is impossible.

Read the Shape of the Spending

From the Black Friday histogram:

• Peak at the $40–60 bin — the most customers
• A long thin tail stretching right toward big spenders

This shape is a slight right skew — and a list of 60 numbers couldn't show it.

Predict: Which One Has Gaps?

Two displays of the same customers:

• A. How they paid — categories: cash, card, check
• B. How much they spent — dollar bins

Which display has gaps between its bars? Decide before advancing.

Bar Graph Versus Histogram Side by Side

• Bar graph: categories → gaps between bars
• Histogram: continuous numbers → touching bars

Bin Width Is a Trade-Off

• Too wide: shape collapses — you learn nothing
• Too narrow: jagged and noisy

Aim for 5–10 bins for most data sets.

Which Bin Width Shows the Shape?

Look back at the two Black Friday histograms.

• Which one reveals the right skew and the peak?
• Which one hides the shape?

Pick the bin width you'd report — and be ready to say why.

Find the Error in This Histogram

A student graphed continuous temperature data like this:

• Bars drawn with gaps between them, like a bar graph

What rule does this break, and how would you fix it?

Your Turn: Build a Full Histogram

Fifty quiz scores ranging from 40 to 100.

1. Choose a sensible bin width
2. Tally the scores into a frequency table
3. Draw the histogram — bars touch, height = count

Then describe the shape in one sentence.

Three Common Traps to Avoid

Dot plot: forgetting to stack repeats hides the frequency
Histogram: gaps between bars means you drew a bar graph
Bins: too wide and the shape disappears

Each turns a correct idea into a wrong picture.

Two Pictures, Two Sizes of Data

✓ Dot plot: every value, best for small sets
✓ Histogram: overall shape, best for large sets
✓ Same number line — different question

Next lesson: the box plot compresses data into five numbers for comparison.