Descriptive Statistics Classroom Activity (40 Min)

The hook, 5 minutes

Project the descriptive statistics calculator before students sit down and do not touch it. It loads with a data set already sitting in the paste box: 2, 3, 3, 4, 4, 4, 5, 5, 6, 8, 11, 17, 26.

Ask the class to predict, from the numbers alone, whether the mean is bigger than 5, smaller than 5, or about equal to 5. Take a show of hands for each option before you click anything. Most classes split three ways, which is the point.

Now scroll to the panel. The median reads 5. The mean reads 7.54. The line under the five-number summary reads "mean above median, so the tail runs right." Ask what pulled the mean up. It is not one freak number, it is the whole run of larger values, 6, 8, 11, 17, and 26, sitting above the median on one side of the distribution. Point out the boxplot too: a single red circle floats past the right whisker. That is the calculator flagging 26 against its own 1.5 times IQR fence, and it becomes the thread the rest of the period pulls on.

Guided exploration on the calculator, 25 minutes

Run these four moves in order. Before every click, students commit to a prediction on paper or a whiteboard. Nobody reveals until every hand has written something down.

1. Click the Symmetric preset. Predict first: will the mean and median be close together, or far apart, for this set? Reveal. The panel reports a mean of exactly 16 and a median of exactly 16, and the shape line reads "mean and median are close, so it looks roughly symmetric." Contrast this out loud against the hook's skewed set: same calculator, same rule, opposite shape.
2. Click the With an outlier preset. The data is 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 68. Before revealing, ask two predictions: will the range grow a lot, a little, or not at all because of the 68, and will the IQR do the same thing. Reveal. Range is 47, driven entirely by one point. IQR is only 4, because Q1 sits at 22 and Q3 sits at 26, and the single high value never touches either quartile. The boxplot makes this visible on its own: a tight box near the left, a long whisker and a lone red circle stretching far to the right.
3. Edit the paste box by hand. With that same set still loaded, delete the trailing ", 68" from the end of the box, so ten values remain: 21, 22, 22, 23, 24, 24, 25, 25, 26, 27. Predict before the panel updates: will removing that one point move the mean more, the median more, or both by about the same amount. Reveal. The mean drops from 27.91 to 23.90, a swing of about 4.01. The median does not move at all, it stays at 24 in both versions, because the middle of an odd or even ordered list does not care how large the largest value gets. This is the single clearest demonstration in the lesson and it is worth running twice if the class wants to see it again.
4. Click the Test scores preset. Fifteen values, 55 through 99. Have students work the five-number summary by hand in pairs first: median, Q1, Q3, IQR, and the two fences. Give them two minutes, then reveal the calculator's version to check: median 79, Q1 71, Q3 88, IQR 17, lower fence 45.5, upper fence 113.5, and Flagged reads "none." Ask why, with a mean of 78.67 sitting just a hair under the median, the shape line still calls this roughly symmetric rather than skewed. The gap between the mean and the median here is small relative to the IQR, which is exactly the comparison the shape line is built to make.

Check for understanding, 5 minutes

In pairs, hand out a fifth data set that never touches the calculator's own presets, so students cannot just remember an answer from the demo: 4, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10.

Ask pairs to find the median, Q1, Q3, and the IQR by hand, then decide whether they expect the calculator to flag any outliers, before typing the numbers in to check. Worked by hand: median is 8, Q1 is 7, Q3 is 9, IQR is 2, and the fences land at exactly 4 and 12. Nothing in the set falls outside those fences, so the calculator should read "Flagged: none," which most pairs get right once they have done the fence arithmetic themselves.

Walk the room while pairs work and listen for the two most common wrong turns: sorting the values incorrectly before splitting them in half, and building the fences from the mean and standard deviation instead of from Q1 and Q3. Both are worth naming out loud once you have heard them, rather than saving the correction for the end of class.

Exit ticket, 5 minutes

Two questions, done individually, no calculator.

1. A data set reads 3, 4, 4, 5, 5, 40. Find the mean and the median by hand, then state which one better describes a typical value in this set and say why in one sentence. (Median is 4.5, mean is about 10.17. The median is the better summary here, because five of the six values sit between 3 and 5, and the mean is pulled far above all of them by the single value 40.)
2. A boxplot shows a red circle above the upper whisker. A student says, "That point must be a mistake." Using only what the 1.5 times IQR rule actually checks, is the student's claim justified? Explain in one or two sentences. (No. The rule flags a value as unusual enough to look at again, it does not diagnose why the value is unusual. The point could be a measurement error, or it could be a real and correct value that is simply extreme, such as the one very long-necked giraffe in a herd of otherwise average heights.)

Collect the slips on the way out. A quick read of question two tells you, faster than any quiz, whether the outlier-rule misconception survived the period.

No-tech variant

For a room without one-to-one devices, a projector outage, or a day you would rather keep every eye off a screen, run the same four moves on paper and on the floor.

Print the four data sets from the guided exploration onto index cards, one value per card. For the Symmetric and With an outlier moves, hand a stack to a small group and have them tape their cards onto a number line drawn on the board, in order, so the class builds a human dot plot by hand. For move three, physically pull the "68" card off the line in front of the class and recompute the median and mean together on the board. The visual of removing one card and watching the median marker not move is close to as strong as the live calculator, and some teachers find it stronger, because the class did the sorting themselves.

For the Test scores move and the check for understanding set, give each pair a printed card with just the values and a blank five-number-summary template (five boxes and two fence lines) to fill in by hand. Collect the templates as your check for understanding instead of watching a screen. The exit ticket questions need no technology in either version and are printed exactly the same way.

Materials

• A projector or shared screen with the descriptive statistics calculator open, or one device per student or pair if you want them clicking along themselves. The calculator needs no account and nothing typed into it leaves the device.
• One printed handout per student or pair carrying the four data sets used in the guided exploration, plus the check for understanding set, each with a blank spot for the five-number summary and the two fences.
• Whiteboards, or scratch paper, for the by-hand computations in moves three and four and in the check for understanding.
• For the no-tech variant: index cards, one value per card, for the Symmetric and With an outlier sets, plus tape and a number line drawn or taped across the board.
• Exit ticket slips, one per student, with the two questions printed ahead of time.

Common misconceptions this lesson targets

1. The mean is not "the average" you always report. Many students learned one procedure called "the average" in earlier grades and reach for it regardless of shape. Move one and the hook are built to force a comparison: report the median instead of the mean whenever the data are skewed or carry an outlier, and say why, pointing at the actual gap between the two numbers rather than reciting a rule.
2. The IQR and the range measure different things, and mixing them up costs points. Range uses only the two most extreme values in the whole set, so a single unusual point can move it by almost any amount. The IQR describes only the middle half of the data and barely reacts when one value at the far edge changes, which move two is built to make visible: an IQR of 4 sitting next to a range of 47 from the same eleven numbers.
3. The 1.5 times IQR rule flags a value, it does not diagnose it. Students often read a red circle on the boxplot as proof that a value is wrong. The rule only marks a point as far enough from the middle 50% of the data to be worth a second look. Whether that point is an error, a rare but real measurement, or evidence of something else in the data collection is a separate question the rule cannot answer, which is exactly what the exit ticket's second question checks for.