You are a data detective! Collect a data set, analyze it with statistics, display it, and write your data story. Every phase builds toward a complete statistical investigation.
You are the class data detective. Work through four phases to carry out a full statistical investigation: classify statistical questions, compute measures of center and variability, display the data, and write a data story. Hit Calculate or Check in each phase, then complete the final checklist and reflection. Print your finished investigation.
A statistical question is one you would collect data to answer — and the data has variability (different people or things give different answers). A non-statistical question has one definite answer.
1. "How many minutes does each student in our class spend reading each day?"
2. "How many pages are in our math textbook?"
3. "What are the heights (in inches) of students on the school basketball team?"
4. "How many days are in a week?"
Ask yourself: "Could different people, objects, or times give different answers?" If yes, the data would vary — so it is a statistical question. If there is one fixed answer (like 7 days in a week), it is non-statistical.
Enter a data set of 6–9 numbers (your own class data, or use the example below). The calculator will find the mean, median, and mode and show every step.
Mean: Add all values, then divide by how many there are.
Median: Sort the values from least to greatest. The middle value is the median. If there is an even count, average the two middle values.
Mode: The value that appears most often. A data set can have no mode, one mode, or multiple modes.
Using the same data set from Phase 2, compute the range (how spread out) and MAD (mean absolute deviation — the average distance each value is from the mean). Show your work.
Range = Maximum value − Minimum value.
MAD steps: (1) Find the mean. (2) Subtract the mean from each value and take the absolute value — that is the deviation. (3) Find the average of all those absolute deviations. That average is the MAD.
Click Draw Dot Plot to see your data set visualized. Then choose the shape that best describes your distribution and check a quick-check problem.
Sort the values: 3, 5, 7, 9, 11. There are 5 values, so the middle one (position 3) is the median.
Distribution shapes: Symmetric means the data is balanced on both sides of the center. Skewed right means a long tail stretches to the right. Skewed left means the tail goes left. Outliers are values much higher or lower than the rest.
Write a 4–6 sentence data story using all your results. Tell a reader what the data shows — use your mean, median, mode, range, MAD, and distribution shape. A good data story explains what the numbers mean in context.
| Category | 4 — Expert | 3 — Proficient | 2 — Developing |
|---|---|---|---|
| Statistical Questions (6.SP.1) | All questions correctly classified with clear reasoning about variability | All or most questions correctly classified | Some questions classified correctly; reasoning unclear |
| Center: Mean, Median, Mode (6.SP.3 / 6.SP.5c) | All three measures correct with work shown; explains which to use and why | All three measures correct | One or two measures correct; minor computation error |
| Variability: Range & MAD (6.SP.5c) | Range and MAD both correct with step-by-step work shown; interprets what spread means | Range and MAD both correct | Range correct; MAD attempted with a step error |
| Display & Shape (6.SP.4 / 6.SP.2) | Dot plot is accurate; distribution shape correctly described and justified | Dot plot accurate; shape identified | Dot plot has minor errors; shape partially described |
| Communication (Data Story) | Data story clearly uses all five measures in context; reader understands the data | Data story uses most measures; meaning is clear | Data story is incomplete or missing context |