Mission 21 Unit 8 6.SP.A.2 · 6.SP.A.3 · 6.SP.B.5c

Center and Spread

6.SP.B.5 · Unit 9
Today's objective: Summarize data with measures of center and variability.
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.

Two sixth-grade classes at Riverside Middle School held a read-a-thon. Class A has 24 students who read 8, 12, 15, 15, 18, 20, 22, 22, 24, 25, 25, 26, 27, 28, 30, 30, 32, 34, 35, 36, 38, 40, 42, 45 books. Class B has 24 students who read 5, 10, 12, 14, 16, 18, 20, 20, 22, 24, 24, 25, 25, 26, 28, 30, 32, 35, 38, 40, 45, 48, 50, 55 books. The principal wants to give an award to the class that "read better overall." Your team must use mean, median, range, and IQR to build a fair comparison and recommend which class earns the award.

Read-a-Thon Results 0 10 20 30 40 50 Books Read Class A 8 Q1=18 Med=25.5 Q3=34 45 Class B 5 Q1=17 Med=24.5 Q3=36.5 55 Class A (n=24) Class B (n=24)

The Problem

Which class "read better overall"? The principal says the winning class gets a pizza party. But "better" could mean different things. Use mean, median, range, and IQR to build your case. Your recommendation must explain which measure(s) you chose and why they are the fairest way to compare.

Visual Model: Side-by-Side Data

Books Read — Dot Plot Comparison 0 10 20 25 35 45 55 Class A Class B Mean A ≈ 27 Mean B ≈ 27

Step-by-Step Investigation Guide

  1. Organize the data. Both data sets are already in order from least to greatest. Count to confirm each class has 24 values. Why does ordering the data first help you find the median and quartiles?
  2. Find the median of each class. With 24 values, the median is the average of the 12th and 13th values. For Class A: (26+27)/2 = 26.5. For Class B: (25+25)/2 = 25. What does the median tell you that the mean does not?
  3. Calculate the mean of each class. Add all values and divide by 24. Class A total = 633, mean ≈ 26.4. Class B total = 646, mean ≈ 26.9. The means are very close. Does that mean the classes performed the same?
  4. Find the range. Range = max - min. Class A: 45 - 8 = 37. Class B: 55 - 5 = 50. Class B has a bigger range. What does that tell you about how spread out its data is?
  5. Find Q1, Q3, and the IQR. Split each half (12 values) and find the median of each half. Class A: Q1=18, Q3=34, IQR=16. Class B: Q1=17, Q3=36.5, IQR=19.5. Which class has scores that are more "bunched together" in the middle 50%?
  6. Make your recommendation. Compare the four measures side by side. Decide which measure(s) are fairest for choosing the "better" class and explain why. Could you argue either class deserves the award? What makes your choice stronger?

Language Support: Key Vocabulary

Mean
The average. Add all numbers, then divide by how many numbers there are.
Median
The middle number when data is in order. If two middle numbers, find their average.
Range
The difference between the highest and lowest values. Shows total spread.
IQR (Interquartile Range)
Q3 minus Q1. It shows the spread of the middle 50% of the data.
Quartile
Values that split ordered data into four equal parts (Q1, Q2=median, Q3).
Outlier
A value that is much higher or much lower than most of the data.
Sentence Frames:

"The mean of Class ___ is ___, which is [higher/lower] than Class ___."

"The IQR of Class ___ is ___, so the middle 50% of scores are [more/less] spread out."

"I recommend Class ___ because ___."

Multiple Representations

Use the box-and-whisker plots in the hero image above. Compare where the boxes overlap and where they differ. Notice that Class A's box is narrower (smaller IQR) while Class B's whiskers stretch further (larger range).

Measure Class A Class B What it shows
Mean ≈ 26.4 ≈ 26.9 Typical value (affected by extremes)
Median 26.5 25 Middle value (not pulled by extremes)
Range 37 50 Total spread of all values
IQR 16 19.5 Spread of middle 50%

Approach: Write a paragraph comparing the two classes using all four measures. Example start:

"Both classes have very similar means (Class A ≈ 26.4, Class B ≈ 26.9), so the average student read about the same number of books. However, Class A has a higher median (26.5 vs. 25), which means more students in Class A read above 25 books. Class B has a much larger range (50 vs. 37) and a larger IQR (19.5 vs. 16), which tells us..."

Team Roles

Facilitator
Read the data sets aloud. Make sure everyone understands the question: "Which class read better?" Keep the team moving through each measure.
Model Builder
Draw the box-and-whisker plots or dot plots on paper. Label min, Q1, median, Q3, and max for both classes.
Precision Checker
Verify every calculation: check the sums for the mean, confirm the median position (12th and 13th values), double-check Q1 and Q3.
Reporter
Prepare the defense statement: "We recommend Class ___ because ___." Include at least two measures as evidence.

Timed Lab Phases

Ready
Click a phase, then press Start.
03:00
  • Read both data sets and the scenario.
  • Assign roles.
  • Underline the key question: What does "read better overall" mean?
  • Checkpoint: Can every team member explain what you need to find?
  • Calculate mean, median, range, and IQR for BOTH classes.
  • Model Builder: create box plots or dot plots.
  • Precision Checker: verify each calculation step.
  • Checkpoint: Do you have all 4 measures for both classes written down?
  • Compare the four measures side by side.
  • Decide: Which measure(s) best answer the question?
  • Write your recommendation with evidence.
  • Checkpoint: Does your recommendation use at least two different measures?
  • Reporter: practice the defense statement aloud.
  • Team: ask each other the defense questions below.
  • Revise if any answer is unclear.
  • Checkpoint: Can the Reporter explain WHY you chose those measures?

Challenge

Extension: A new student joins Class B and read 100 books. Recalculate the mean, median, and range for Class B. How does one extreme value change your recommendation?
What If...?
  • What if you removed the highest and lowest score from each class? Would your recommendation change?
  • What if the principal said "the class where most students read above 25 books"? Which measure helps most?

Real-Life Connection: Sports analysts use mean, median, and IQR to compare players. A player with a high mean but huge range is "inconsistent." Coaches prefer consistent performers — just like you might argue one class is "more consistently strong."

Defense Preparation

  1. Which statistical measure did you rely on most, and why? "We focused on ___ because it shows ___."
  2. The means are almost the same. How did you break the tie? "Even though the means are close, the ___ tells us ___."
  3. How does the IQR help you understand consistency? "A smaller IQR means the middle 50% of students scored between ___ and ___, which shows ___."
  4. Could someone argue for the other class? How would you respond? "Someone might say Class ___ is better because ___, but we disagree because ___."
Rubric Quick-Check:
  • All 4 measures calculated correctly for both classes
  • Visual model (box plot or dot plot) is labeled
  • Recommendation uses at least 2 measures as evidence
  • Defense answers explain "why this measure" not just "what the number is"

Exit Product

Submit a one-page Lab Report that includes:
  • A summary table with all 4 measures for both classes
  • At least one visual model (box plot, dot plot, or histogram)
  • A 2-3 sentence recommendation naming which class "read better" and why
  • One sentence about what would change if an outlier were added
Self-Assessment:
  • I can explain what mean, median, range, and IQR each measure
  • I can compare two data sets using center AND spread
  • I can explain why different measures might lead to different conclusions
  • I can show my thinking with a visual model

Work Space

Calculations:



Visual Model:



Recommendation and Defense: