Dot Plots and Histograms

In this lesson:

• Build a dot plot where every value is visible
• Group data into bins to make a histogram
• Read center, spread, and shape from both plots

What You Will Learn Today

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

1. Construct a dot plot from a small data set with every value correctly placed
2. Construct a histogram by choosing equal-width bins, tallying counts, and drawing bars
3. Read center, spread, and shape from a dot plot
4. Read center, spread, and shape from a histogram
5. Choose between a dot plot and histogram given the data size and question

A List That's Hard to Read

Here are 25 sixth-grader heights in inches:

52, 54, 54, 55, 55, 55, 56, 56, 56, 56, 57, 57, 57,
58, 58, 58, 59, 59, 60, 60, 61, 62, 63, 63, 65

Where does most of the data cluster? What's the spread? Hard to tell just by looking.

You Already Know This Plot

25 heights on a number line — one dot per value, duplicates stacked

Dot Plots Preserve Every Value

• Every value is recoverable — the plot is lossless
• Read exact counts: "four students were exactly 56 inches"
• Center: tallest column around 56–57
• Spread: 52 to 65 — range of 13 inches
• Shape: slight right tail (65 stands apart)

Constructing a Dot Plot Step by Step

Step 1: Draw a number line from 50 to 66

Step 2: For each value, place one dot directly above its position

Step 3: When a value repeats, stack the dot vertically

Step 4: Count all dots — should equal 25 ✓

Quick Check: Reading the Dot Plot

How many students were exactly 56 inches tall?

The Answer: Four Students at 56 Inches

The dot plot shows 4 dots stacked above the value 56.

A histogram will tell us "7 students were in the 56–58 bin" — but it cannot tell us how many were exactly 56 vs. exactly 57.

That's the trade-off we're about to make.

When the Dot Plot Stops Working

What if we had 250 heights instead of 25?

• Stacks would be impossibly tall
• Individual values would be lost in the crowd

The histogram trades individual values for readable shape — at any scale.

Bins Slice the Number Line Evenly

• A bin = an interval on the number line: [56, 58)
• Bin width = interval length — we'll use width 2
• [56, 58): 56 is included, 58 goes to the next bin

The Completed Histogram: Bars Touch

Bars touch — bin boundaries are points on a number line, not gaps between categories

Bin Width Changes the Shape You See

• Width 1: each integer its own bin — like a column version of the dot plot
• Width 2: reveals the peak and slight right tail — useful shape
• Width 5: three fat bars — shape washed out, peak hidden

Predict: Gaps Between Bars — Correct?

A classmate's histogram has gaps between every bar.

• A. Yes — gaps show some heights are missing
• B. No — histogram bars must always touch

Choose A or B before the next slide.

Histograms Touch; Bar Charts Have Gaps

Label bin edges, not bar centers.

Sketch This Histogram from Bin Counts

Sketch: bin edges on x-axis, count on y-axis, bars touching. Try before advancing.

Identify Three Histogram Errors Below

A student's histogram has these problems:

• Labels at bar centers (5, 7, 9, 11, 13) instead of edges
• Gaps between bars
• Bar over [8, 10) is twice as wide as the others

Build Both Plots Without Scaffolding

12 typing speeds (wpm): 28, 31, 31, 34, 34, 34, 36, 38, 38, 40, 43, 47

1. Build a dot plot — number line from 25 to 50
2. Build a histogram — bin width 5: [25,30), [30,35), [35,40), [40,45), [45,50)

Compare What Each Plot Reveals

• Dot plot: How many values are exactly 34? What are they?
• Histogram: What is the bar height over [30, 35)?

The dot plot answers exact-value questions. The histogram answers bin-count questions.

Dot Plots and Histograms: Key Ideas

✓ Dot plot — lossless, one dot per value, small n

✓ Histogram — equal-width bins, bars touch, any n

✓ Bin width changes the shape you see — choose carefully

Bars touch (histogram) vs. gaps (bar chart)

Bar height = count in that bin

What's Next: Box Plots in Lesson 2

In Lesson 2 you'll compute the five-number summary, construct a box plot, and choose the right plot for any question.

Same 25 heights — we'll find the middle half in seconds.