Teacher Cheat Sheet — Session 5: Understanding Averages

Data Science for Young Minds · Grade 4 · Ages 9–10

~60 min Ages 9–10 Session 5 of 8 ND-Friendly

Session Agenda

Time	Block	What's Happening
0–5	Hook	Write 7 numbers on board: 4, 7, 3, 9, 7, 5, 7. "Which single number best represents this group?" Collect guesses.
5–25	Lesson	Mean (step-by-step) · Median (physical number cards) · Mode (most frequent) · Range (max − min)
25–42	Activity	Students calculate all 4 measures for dataset of 7 numbers; compare and discuss which best tells the "story"
42–52	Discussion	"Which measure would a teacher prefer for report cards? Which would a student prefer?" When is each most useful?
52–58	Write	Students write which measure best fits their data set and why — with a specific reason
58–60	Close	Exit ticket: "Name one situation where the median is better than the mean."

Pacing note: Keep the worked example on the board for the ENTIRE session. Students will need to refer back while calculating independently. Do not erase until the session ends.

Materials Needed

Number cards 1–10 (one set per student or pair) Worksheets with calculation spaces Pencils Optional: calculators for checking (not required)

Dataset for activity: 4, 7, 3, 9, 7, 5, 7 (these numbers are chosen so mean=6, median=7, mode=7, range=6 — clean whole numbers throughout)

Key Vocabulary

Mean — add all values, divide by how many there are (the "average")

Median — the middle value when data is ordered from least to greatest

Mode — the value that appears most often

Range — the difference between the maximum and minimum values

Typical value — a number that represents what is "normal" or "usual" in the data

Worked Example — Keep on Board All Session

Dataset: 4, 7, 3, 9, 7, 5, 7 (7 values)

MEAN: Add all values → 4+7+3+9+7+5+7 = 42 · Divide by count → 42 ÷ 7 = 6

MEDIAN:Order values → 3, 4, 5, 7, 7, 7, 9 · Middle value (4th of 7) = 7

MODE: Which value appears most? → 7 appears 3 times = 7

RANGE: Max − Min → 9 − 3 = 6

Results: Mean = 6 · Median = 7 · Mode = 7 · Range = 6

Note for discussion: Mean (6) is lower than median and mode (both 7) because the low value of 3 pulls it down. This is a great example of when median tells a "truer" story than mean for this particular data.

Discussion Questions + Teacher Notes

"If a teacher wants to know how the class 'typically' did on a test, which measure should they use?"
→ Usually median or mean — both give a sense of the middle. But if one student scored 10 and everyone else scored 5, the mean gets pulled up unfairly. Median would be more honest. Push students to think about extreme values.
"If one student scored 100 and the rest scored 60, how does the mean change? How does the median change?"
→ The 100 pulls the mean up significantly but barely moves the median. This is the core "outlier" concept without using that word yet. Students can feel the difference intuitively.
"Can there be more than one mode? Can there be no mode?"
→ Yes to both. If two values tie for most frequent = two modes (bimodal). If every value is different = no mode. This often surprises students — give an example of each.
"Why do we need range if we already have mean, median, and mode?"
→ Range tells us about spread, not center. Two datasets can have the same mean but very different ranges — one tightly clustered, one widely spread. Range adds a crucial second dimension to our description.
"Which single number would YOU use to describe this dataset? Why?"
→ No right answer — but reasoning must use the data. Encourage: "I'd use the median because the 3 and 9 pull the mean away from where most values sit."

Activity Setup + Answer Key

Students use the same dataset (4, 7, 3, 9, 7, 5, 7) to calculate all four measures independently. Physical number cards help with median. Steps should mirror the worked example exactly.

Physical card activity for median:

Write each value on a card: 4, 7, 3, 9, 7, 5, 7
Arrange cards in order on desk: 3, 4, 5, 7, 7, 7, 9
Remove one card from each end simultaneously
Keep removing pairs until one card remains = median (7)

Answer Key:
Mean: 4+7+3+9+7+5+7 = 42 ÷ 7 = 6
Median: ordered → 3,4,5,7,7,7,9 = 7
Mode: 7 appears 3 times = 7
Range: 9 − 3 = 6
Note: mean ≠ median here — great discussion point!

When is each most useful? Mean = balanced datasets with no extreme values · Median = when one extreme value would distort the picture · Mode = categorical data or finding the most popular item · Range = describing variability/spread

Opening Hook

Write on board: 4, 7, 3, 9, 7, 5, 7

"If someone asks 'what's a typical number in this group?' — what would you say? Just one number."

Collect answers. Many will say 7 (mode/median). Some might try to average mentally. Point out: there's more than one way to find a "typical" number — and each tells a slightly different story.

When to Use Each Measure

Mean — balanced data, no extreme outliers (class test average)

Median — one extreme value present (house prices, salaries)

Mode — most popular choice (most common shoe size ordered)

Range — describing spread/variability (weather variation)

ND-Friendly Tips

Physical number cards for median — removing cards from each end is kinesthetic and self-checking. Students can feel when one card is left.
Step-by-step worked example stays on board — do not erase. Students refer back throughout independent work.
Mean calculation scaffold — write the addition sum and division separately as two steps. Avoid combining into one line.
Color-code each measure — Mean = blue, Median = green, Mode = purple, Range = orange. Consistent color helps students track which is which.
Allow calculator for mean — the concept matters more than the arithmetic. If a student struggles with long addition, let them use a calculator and focus on the interpretation step.