Math practice · Unit #03 · both grades · The scientific method

Data or It Didn't Happen

The scientific method is a loop, and numbers are what go around it. Expected vs. observed, mean vs. median, honest graphs vs. lying ones — the toolkit you'll use every week this year starts here.

skills: expected vs. observed mean & median graph literacy ≈ 30 min
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Part A

Expected = what the model predicts. Observed = what the trial actually produces. Sample size = how many trials are counted.

Part B

Mean = fair-share average. Median = middle after ordering. Outlier = unusual value that can pull the mean.

Part C

Axis = a numbered graph edge. Scale = the counting pattern. Units = what the numbers measure.

Part D

Comparison = what a claim is measured against. Funder = who paid for the study. Bias = a pattern that can tilt the evidence.

PART A

Is this coin fair?

A fair coin should land heads 50% of the time — that's the What the mathematical model predicts should happen. result. What you actually flip is the What the experiment actually produces and records. result. Science is mostly the argument between those two.

Flip results
DatasetFlipsHeads% heads
Your 10 flips107
Whole class pooled240118

  1. Fill in the % heads column (round to one decimal).

  2. Which dataset is closer to the expected 50%? Which one should we trust more — and why does a larger The number of trials, people, or measurements included in the data. beat louder opinion?

  3. Expected heads in 240 flips = 120. We observed 118. How far off is that, in flips? As a percent of 240? Is the coin suspicious — or is that just chance doing chance things?

PART B

Mean vs. median: the gust of wind

Paper-airplane trials: three throws measured in meters. Before calculating, use The fair-share average: add every value, then divide by how many values there are., The middle value after the data are ordered from least to greatest., and A value unusually far from the rest of the data.. One throw caught a lucky gust off the vent.

Throw distances (m)
Throw 1Throw 2Throw 3 (the gust)
6.25.814.1

  1. Compute the mean of the three throws.

  2. Find the median (middle value).

  3. Which number better represents "a typical throw" of this plane? What did the outlier do to the mean? Why do scientists report the median when data has wild values?

PART C

Graph detective

Three graphs, three lies. An A numbered edge of a graph that tells what is being measured. needs a fair The counting pattern used to space numbers on an axis., and graph The label for what the numbers measure, such as centimeters or seconds. tell us what the data mean. Name the trick and state the fix that would make the graph honest.

  1. A bar chart of plant growth starts its y-axis at 14 cm instead of 0, so a 15.2 cm bar towers over a 14.8 cm bar like a skyscraper over a shed. The trick? The fix?

  2. A line graph shows "average speed" rising over trials — but the y-axis has no units and no labels, just a line going up. Up in what? The trick? The fix?

  3. A pie chart shows survey results with slices labeled 40%, 35%, 35%, 20%. Add them up. The trick? The fix?

PART D

Demand the numbers

"4 out of 5 dentists recommend ChewMore gum." Sounds scientific. A scientist asks four questions before believing anything. Write one question you'd demand answered about each of these:

  1. How many people or measurements were actually included? — how many dentists were actually asked?

  2. The other choice, group, or condition used as the reference point. — recommended instead of what?

  3. Who paid — why might the The person or organization that paid for the study and may care about its outcome. care about the answer?

Answer key — teachers

Part A

70.0% · 49.2%.

  1. (above)
  2. The pooled 240 flips — big samples wash out lucky streaks; small samples are all streak.
  3. 2 flips off; 2 ÷ 240 ≈ 0.8% off. Not suspicious — this is ordinary chance wobble.

Part B

  1. Mean = (6.2 + 5.8 + 14.1) ÷ 3 = 26.1 ÷ 3 = 8.7 m
  2. Median = 6.2 m
  3. The median — the gust dragged the mean up to 8.7, farther than the plane ever really flew on a normal throw. Median resists outliers.

Part C

  1. Truncated axis — tiny differences look huge. Fix: start the axis at 0.
  2. Missing units/labels — "up" is meaningless without them. Fix: label both axes with units.
  3. Slices sum to 130% — impossible for one pie. Fix: percentages of one whole must total 100%.

Part D

Accept any sharp version of: How many were surveyed (5? 500?)? What were the other options (sugarless vs. sugared? brushing vs. not?)? Who funded the study and what do they sell?