Mission 20 · Unit 8

Data Displays

6.SP.B.4 · Unit 9
Today's objective: Display numerical data in plots on a number line.
Need a hint?
Re-read the problem and underline the numbers and the question. Pick one representation (model, table, or equation), show your steps, and check that your answer makes sense for the situation.

The PE teacher recorded how many push-ups each of the 20 students in the class completed in one minute. The data is: 8, 12, 15, 10, 22, 14, 18, 11, 9, 16, 20, 13, 15, 17, 12, 14, 19, 10, 15, 21. Your team must display this data three ways: a dot plot, a histogram, and a box plot. Then recommend which display best shows the class performance and why.

Push-Up Data: 3 Displays Dot Plot 8 10 12 14 16 18 20 22 Histogram 6 8 6 8-12 13-17 18-22 Box Plot 8 10 12 14 16 18 20 22 Min=8 Q1=11 Med=14.5 Q3=18 Max=22

The Investigation

The Problem: Display the push-up data (20 values) three ways: dot plot, histogram (intervals of 5), and box plot. For the box plot, find the minimum, Q1, median, Q3, and maximum. Then write a recommendation: which display best shows how the class performed, and why?

The Data (ordered)

Position 1 2 3 4 5 6 7 8 9 10
Value 8 9 10 10 11 12 12 13 14 14
Position 11 12 13 14 15 16 17 18 19 20
Value 15 15 15 16 17 18 19 20 21 22

Visual Model: Three Data Displays Compared

Five-Number Summary for the Box Plot Minimum 8 Q1 11 Median 14.5 Q3 18 Maximum 22 How to find the five-number summary: 1. Order the data from least to greatest (already done above). 2. Median = average of 10th and 11th values = (14 + 15) / 2 = 14.5 3. Q1 = median of lower half (positions 1-10) = average of 5th and 6th = (11 + 12) / 2 = 11.5 ≈ 11 Q3 = median of upper half (positions 11-20) = average of 15th and 16th = (17 + 18) / 2 = 17.5 ≈ 18 Dot Plot Shows every data point Easy to see clusters Best for small data sets See exact values Best for: individual values Histogram Groups data in intervals Shows shape of data Good for large data sets See distribution pattern Best for: overall shape Box Plot Shows 5-number summary Easy to compare 2 groups Shows spread (IQR) Hides individual values Best for: comparing groups

Step-by-Step Investigation Guide

  1. Order the data. Write all 20 values from least to greatest. Count to make sure you have exactly 20. Guiding question: What is the smallest value? The largest?
  2. Create the dot plot. Draw a number line from 8 to 22. Place one dot above the number for each data point. Stack dots when values repeat. Guiding question: Which value has the most dots? What does that tell us?
  3. Create the histogram. Make three intervals: 8-12, 13-17, 18-22. Count how many values fall in each. Draw bars with heights matching the counts. Guiding question: Which interval has the most students?
  4. Find the five-number summary. Min = 8. Max = 22. Median = average of 10th and 11th values. Q1 = median of lower half. Q3 = median of upper half. Guiding question: Why do we average two numbers for the median when there are 20 values?
  5. Create the box plot. Draw a number line. Mark the five values. Draw the box from Q1 to Q3, line at the median, whiskers to min and max. Guiding question: Where does the "middle 50%" of the data live?
  6. Compare and recommend. Which display best shows class performance? Why? Guiding question: If the PE teacher wants to see how many students did 15+, which display is easiest to read?

Language Support: Key Vocabulary

Dot plot
A number line with dots above each value. Each dot = one data point.
Histogram
A bar graph that groups data into intervals. Bars touch each other.
Box plot
A display that shows the five-number summary as a box with whiskers.
Median
The middle value when data is ordered. Half the data is above, half below.
Quartile (Q1, Q3)
Values that split data into four equal parts. Q1 = lower quarter. Q3 = upper quarter.
Interval
A range of values grouped together, like 8-12 or 13-17.
Sentence Frames:

"The dot plot shows that the most common push-up count is _____ because _____."

"The histogram shows that the interval _____ has the most students."

"The box plot tells me the middle 50% of students did between _____ and _____ push-ups."

Multiple Representations

Approach 1: Dot Plot (see every value)

Each dot is one student. You can see that 15 push-ups is the most common (3 dots). The spread goes from 8 to 22. Clusters appear around 10-15.

Approach 2: Histogram (see the shape)

Three bars: 8-12 has 6 students, 13-17 has 8 students, 18-22 has 6 students. The data is roughly symmetric with the peak in the middle interval.

Approach 3: Box Plot (see the summary)

Min=8, Q1=11, Median=14.5, Q3=18, Max=22. The IQR (Q3-Q1) = 7. The middle 50% of students did between 11 and 18 push-ups. The range is 14.

Team Roles

Facilitator Read the push-up data aloud while the team orders it. Assign one display to each partner pair. Keep the team on schedule.
Model Builder Draw all three data displays. Use a ruler for the number lines. Make sure all axes are labeled and scaled correctly.
Precision Checker Count dots on the dot plot (must equal 20). Verify histogram bar heights add to 20. Check the five-number summary calculations.
Reporter Prepare the defense: explain what each display shows, state the five-number summary, and present the team's recommendation.

Timed Lab Phases

Launch Phase
03:00

Read the PE scenario. Assign roles. Order the 20 data values from least to greatest.

  • How many data points are there?
  • What is the smallest and largest value?
  • What do you predict the typical push-up count is?
Checkpoint: Data is ordered. Everyone knows min=8 and max=22.

Create the dot plot and histogram. Find the five-number summary.

  • Dot plot: does your total dot count = 20?
  • Histogram: do your bar heights add to 20?
  • Five-number: Min, Q1, Median, Q3, Max?
Checkpoint: Dot plot + histogram drawn. Five-number summary calculated.

Draw the box plot. Compare all three displays. Write your recommendation.

  • Is the box plot box drawn from Q1 to Q3?
  • Is the median line inside the box?
  • Which display answers the PE teacher's question best?
Checkpoint: All 3 displays complete. Recommendation written with reasoning.

Reporter prepares the defense. Show all three displays and explain the recommendation.

  • "The dot plot shows _____ because _____."
  • "The histogram shows _____ because _____."
  • "The box plot shows _____ because _____."
  • "We recommend _____ because _____."
Checkpoint: Defense explains each display's purpose and states a clear recommendation.

Challenge Extensions

Extension Problem: Another PE class had these push-up results: Min=5, Q1=9, Median=12, Q3=15, Max=25. Draw a box plot for this class on the same number line as your class. Compare the two classes: which class is stronger overall? Which class has more spread?

What If?

  • What if one student did 45 push-ups? How would that outlier change each display?
  • If you changed the histogram intervals to groups of 3 instead of 5, would the shape look different?
  • Which display would you use to compare boys and girls in the same class? Why?

Real-Life Connections

Data displays appear in weather reports (temperature histograms), sports (player stat box plots), health (BMI dot plots), and business (sales dashboards).

Defense Preparation

  1. What is the five-number summary? Name all five values.
  2. What does each display show that the others do not?
  3. What is the IQR? What does it tell us about the class?
  4. Which display do you recommend and why?
Sentence Starters:
  • "The five-number summary is: Min=_____, Q1=_____, Median=_____, Q3=_____, Max=_____."
  • "The dot plot is best for _____ because _____."
  • "The IQR is _____, which means the middle 50% of students _____."

Rubric

Criteria Excellent (4) Proficient (3) Developing (2)
Dot plot All 20 dots correct, labeled axis Minor dot error, axis present Plot attempted
Histogram Correct bars with labels and title Correct bars, partial labels Bars attempted
Box plot 5-number summary correct, box accurate Minor calculation error Box attempted
Recommendation Clear choice with display-specific reasoning Choice with general reasoning Choice stated only

Exit Product

Your team submits: A Data Display Poster with:
  • Ordered data list (all 20 values from least to greatest)
  • A dot plot with labeled number line and all 20 dots
  • A histogram with 3 intervals, labeled axes, and title
  • The five-number summary: Min=8, Q1=11, Median=14.5, Q3=18, Max=22
  • A box plot drawn from the five-number summary
  • A written recommendation: which display is best for the PE teacher and why

Self-Assessment Checklist