Neft Teacher · Learn It

Unit 2 · Standard 6.DS.5

Represent and Describe Data in a Histogram

Lesson 2-2 · Learn It — how the math works

Why we're learning this

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!

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Learn It

What is a histogram?

A histogram is a bar graph that groups numbers into equal ranges called intervals. The height of each bar is the frequency: how many values fall in that interval. The bars touch because the intervals are continuous.

Picture itSee what the math looks like before you read about it

A basketball league tracked the points-per-game average for all 30 of its players this season. The histogram groups those averages into equal intervals of 10 points.
Where you see this in real lifeA basketball league tracked the points-per-game average for all 30 of its players this season. The histogram groups those averages into equal intervals of 10 points.
League Scoreboard — Points Per Game (30 players)
2578910111112131314141515161617181819202122232425283032
Each tile is one player's scoring average.

Watch me solve itI do — read one step at a time

The problem looks like this
Histogram of the data 3, 7, 12, 15, 18, 24 in intervals of 10: 0–9 has 2, 10–19 has 3, 20–29 has 1.00.511.522.530102030ValueFrequency
  1. My data: 3, 7, 12, 15, 18, 24. I will use of 10: 0–9, 10–19, 20–29.
  2. 0–9: the values 3 and 7 fit, so the is 2.
  3. 10–19: the values 12, 15, and 18 fit, so the is 3.
  4. 20–29: only the value 24 fits, so the is 1.
  5. Now I draw three bars with heights 2, 3, and 1, touching each other. The tallest bar (10–19) is where most values are.

Watch out — mistakes students make here

  • Compare: 2, 5, 10, 8, 3—the largest is 10.
  • 80–89 has 8 students, but 8 is less than 10. Which interval has the tallest bar?
  • A symmetric shape would have the bars mirroring each other around the center. Compare the 9 at the low end with the 1 at the high end.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. New data: 2, 4, 8, 11, 13, 16, 21. We will use of 10 again: 0–9, 10–19, 20–29.
  2. How many values fall in 0–9?
    Check this step
    Count them. How many fall in 10–19?
  3. How many fall in 20–29?
    Check this step
    Which would have the tallest bar?

On your ownYou do — solve this one by yourself

Solve: A of test scores shows: 50–59: 2, 60–69: 5, 70–79: 10, 80–89: 8, 90–99: 3. Which has the most students?

My answer

Stuck? Open one hint at a time.

Hint 1

'Most students' means the highest frequency — compare the counts 2, 5, 10, 8, 3, not the score ranges themselves.

Hint 2

Careful: the highest scores (90–99) don't mean the most students. Find the largest of the five frequencies first, then read off its interval.

Hint 3

First step: circle the largest number among 2, 5, 10, 8, 3. Then match that count back to its interval — and check the choice pairs both parts.

Check my answer
✅ Answer: 70–79 with 10 students
The 70–79 interval has the highest frequency of 10 students.

Turn & TalkSay it out loud with a partner

You have 30 players' points-per-game averages. Why is it easier to display them in a with than to list all 30 numbers?

Try starting with:

  • A histogram is easier because it groups the data into ___.Un histograma es más fácil porque agrupa los datos en ___.
  • Each bar shows how many players fall in that ___.Cada barra muestra cuántos jugadores caen en ese ___.
Use these wordshistogramfrequencyintervaldistributionbar