Unit 8 · Standard 6.SP.4
Display Data: Histograms
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
Bars side by side: 0-9 pts (3 players), 10-19 pts (8 players), 20-29 pts (4 players)
Histogram
A bar graph that groups data into equal ranges. The bars touch.
If 5 players scored 10-19 points, the frequency for that interval is 5
Frequency
How many times a value shows up.
0-9, 10-19, 20-29 are intervals of width 10 — each covers 10 values
Interval
A range of numbers used to group data.
Most data in the middle with fewer at the ends = bell-shaped; most on one side with a tail = skewed
Distribution
How the data is spread out.
A histogram that is tallest in the middle and shorter on both sides is symmetric
Data distribution
How the data looks: where it sits and how spread out it is.
Data in just 2 intervals = low variability. Data across 6 intervals = high variability
Variability
How spread out the numbers are.
Key Ideas & Notes
- The basketball league has 30 players and wants to display everyone's points-per-game average in a way that shows how the data is distributed.
- The raw averages are: 2, 5, 7, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 25, 28, 30, 32.
- Listing all 30 numbers is hard to read — a histogram will reveal the pattern!
Think About It
- Where do most of the scoring averages seem to cluster?
- Are there many players at the very low or very high end?
- How could you group these numbers to see a pattern?
My Notes
Guided Examples
Example 1
A histogram shows these frequencies: 0–4: 3 players, 5–9: 8 players, 10–14: 12 players, 15–19: 5 players. How many players are represented in total?
Solution: Add all frequencies: 3 + 8 + 12 + 5 = 28 players.
Answer: A. 28
Example 2
In a histogram, what does the height of each bar represent?
Solution: Each bar's height shows the frequency — how many data values fall within that interval.
Answer: A. The frequency (count) of data in that interval
Example 3
How is a histogram different from a regular bar graph?
Solution: In a histogram, bars touch because each interval connects to the next (0–9, 10–19, etc.) — the data is continuous.
Answer: A. Histogram bars touch (no gaps) because the intervals are continuous ranges
Write About the Math The Writing Revolution
I can explain my histogram using the words histogram, frequency, interval, and distribution.
1. Kernel Sentence subject + verb
Model: Histogram is a bar graph that groups data into equal ranges. The bars touch.Histograma es una gráfica de barras que agrupa datos en rangos iguales. Las barras se tocan.
Write a kernel sentence about histogram. Use a subject and a verb.Escribe una oración base sobre histograma. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Histogram matters in mathHistograma importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Histogram matters in math because ___.Histograma importa en matemáticas porque ___.
Histogram matters in math, but ___.Histograma importa en matemáticas, pero ___.
Histogram matters in math, so ___.Histograma importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about histogram.Di un hecho verdadero sobre histogram.
Histogram ___.
Ask a question about histogram.Haz una pregunta sobre histogram.
How does ___ ?¿Cómo ___ ?
Show excitement about histogram.Muestra entusiasmo sobre histogram.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with histogram.Dile a un compañero qué hacer con histogram.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
A histogram groups data into ___.Un histograma agrupa los datos en ___.
The tallest bar shows ___.La barra más alta muestra ___.
This helps when ___.Esto ayuda cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. A histogram has intervals: 0–4, 5–9, 10–14, 15–19. What is the width of each interval?
- 5
- 4
- 10
- 19
2. A histogram of test scores shows: 50–59: 2, 60–69: 5, 70–79: 10, 80–89: 8, 90–99: 3. Which interval has the most students?
- 70–79 with 10 students
- 80–89 with 8 students
- 60–69 with 5 students
- 90–99 with 3 students
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A teacher collected test scores and made two different histograms — one with intervals of 5 (50–54, 55–59, etc.) and one with intervals of 20 (50–69, 70–89, 90–109). Both use the same data. How might the two histograms look different? Which interval size gives you more detail about the distribution? When might the larger interval be better?
Sentence starter: The histogram with intervals of 5 would have ___ bars and show ___. The histogram with intervals of 20 would have ___ bars and show ___. Smaller intervals are better when ___, and larger intervals are better when ___.
Reflect — Exit Ticket
A histogram of player heights shows: 60–63 in: 2, 64–67 in: 7, 68–71 in: 9, 72–75 in: 4. Which interval has the most players?
- 68–71 inches
- 64–67 inches
- 72–75 inches
- 60–63 inches
Answer Key & Teacher Guide
- Try It 1: A. 5 — Each interval covers 5 values (0,1,2,3,4 then 5,6,7,8,9 etc.), so the width is 5.
- Try It 2: A. 70–79 with 10 students — The 70–79 interval has the highest frequency of 10 students.
- Exit Ticket: A. 68–71 inches — The 68–71 inch interval has the highest frequency of 9 players.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Histogram is a bar graph that groups data into equal ranges. The bars touch.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).