Data Detective

A data detective solves cases with a pipeline, not a magnifying glass. This lesson runs one small case from scratch: pose a good question, gather evidence, compute three averages, interrogate one suspicious value, pick an honest chart, and write a conclusion that survives cross-examination.

Case open: one good question

A survey question must be answerable with numbers. "Do classmates like chores?" cannot be measured; "How many chores did you do at home yesterday?" can be answered, recorded and compared. Whom you ask matters too: three deskmates cannot speak for the whole class. The craft of questionnaires lives in Surveys & Sampling. Suppose we asked a group of 12.

Collect: keep the 12 numbers safe

The raw data as registered: 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 7, 16.

InteractiveEvidence Desk

Count

Mean

6.14

Median

Mode

Clear the explorer's existing numbers and add these 12 one by one (click a number to remove it), watching the dot plot and the three averages:

mean: the total is $60 \div 12 = 5$ ;
median: after sorting, the two middle values are 4 and 4, so 4;
mode: the most frequent value is 4, appearing 4 times.

The basics behind all three live in Mean, Median & Mode.

Judge the suspect: that 16

Every other value crowds between 2 and 7, while 16 stands alone. A detective's first move is not deleting — it is verifying: did someone truly do 16 chores, or was a 6 miscopied as 16?

Three treatments, three verdicts

Keep the 16: mean 5, median 4, mode 4;
correct it to 6: mean $50 \div 12 \approx 4.2$ , median 4, mode 4;
drop it: mean $44 \div 11 = 4$ , median 4, mode 4.

One suspicious value drags the mean from 4 up to 5, while the median does not budge — that is its armor. The honest move: verify first; if you cannot, report both outcomes and disclose the pending extreme value.

Present and close the case

InteractivePresentation Desk

The same data tells different stories in different charts: a bar chart compares heights, ideal for comparing counts across categories; a pie chart shows shares, ideal for how each part relates to the whole. Anyone wanting to exaggerate will also fiddle with axes and slices — the tricks are catalogued in Misleading Graphs. Finally, write a conclusion with numbers, a range, and the courage to admit uncertainty:

Yesterday these 12 students helped with chores a median of 4 times, most between 3 and 5; one reported 16 — the mean waits until that number is verified.

A good conclusion always survives the question "how did you compute that?"

Check yourself

Quick quiz

1. For 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 7, 16 — what is the mean?
2. The 16 turns out to be a miscopied 6. After correcting it, which average stays the same?
3. Which chart best shows each type of chore as a share of all chores?