Neft Teacher · Learn It

Unit 2 · Standard 6.DS.5

Represent and Describe Data in a Box Plot

Lesson 2-4 · Learn It — how the math works

Why we're learning this

The basketball league wants to compare scoring across teams. Here are the points scored by each player on the Wildcats in their last game: 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28. The league needs a quick visual that shows the spread, the middle 50%, and any high or low scorers. Time to build a box plot!

✱ Math Workbench

Learn It

What is a box plot?

A box plot is a simple picture that shows how a set of data is spread out, using just five key numbers: the lowest value, the first quartile (Q1), the median (middle), the third quartile (Q3), and the highest value.

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

The table shows 25 sixth graders' times to finish a 5-kilometer road race.
Where you see this in real lifeThe table shows 25 sixth graders' times to finish a 5-kilometer road race.

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

The problem looks like this
Box plot: minimum 4, Q1 8, median 14, Q3 22, maximum 28.481216202428
  1. My data, in order: 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28. There are 11 numbers.
  2. The middle number is the 6th one, 14, so the = 14.
  3. The lower half is 4, 6, 8, 10, 12. Its middle is 8, so Q1 = 8.
  4. The upper half is 15, 18, 22, 24, 28. Its middle is 22, so Q3 = 22.
  5. The lowest is 4 and the highest is 28. I draw a box from 8 to 22, a line at 14, and out to 4 and 28.

Watch out — mistakes students make here

  • 28 is the midpoint — IQR is Q3 − Q1, the spread.
  • 36 is just Q3 — subtract Q1 to find the range between them.
  • IQR subtracts Q1 from Q3, it doesn't add them.

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

Same steps, new numbers.

  1. New, smaller data set: 2, 5, 5, 8, 11. First, what is the (the middle value)?
  2. The lower half is 2, 5 and the upper half is 8, 11. What is Q1?
    Check this step
    What is Q3?
  3. What are the lowest and highest values?
    Check this step
    Now picture the box stretching from Q1 to Q3 with the line inside.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Now find the for a DIFFERENT team — the Comets: 2, 6, 10, 12, 16, 18, 22, 24, 26, 30, 34.
  • Place Min, Q1, , Q3 and Max on the number line, then try the practice problems.

Solve: Two show: Team A has IQR = 8, Team B has IQR = 22. What does this tell you?

My answer

Stuck? Open one hint at a time.

Hint 1

IQR measures the width of the box — how spread out the MIDDLE 50% of each team's scores is.

Hint 2

Compare a narrow box (IQR 8) with a wide box (IQR 22). Ask what narrow vs wide says about consistency — not about which team is better.

Hint 3

First step: translate each number — Team A's middle scores span only 8 points; Team B's span 22. Then choose the statement that matches.

Check my answer
✅ Answer: Team A's middle 50% is more consistent; Team B's is more spread out
A smaller IQR means the middle 50% of data is more tightly clustered. Team A's scoring is more consistent in the middle range.

Turn & TalkSay it out loud with a partner

The Wildcats' scores are 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28. To build a you need a . What five numbers will you need?

Try starting with:

  • A box plot needs the ___, Q1, median, Q3, and ___.Un diagrama de caja necesita el ___, Q1, mediana, Q3 y el ___.
  • The median of these scores is ___.La mediana de estos puntajes es ___.
Use these wordsbox plotmedianquartileinterquartile rangeminimum