Choose a real-world topic, pose a statistical question, analyze a data set, describe the spread, pick the best display, and write your investigation report.
You are a data investigator. Choose a real-world dataset (sports, weather, or survey), pose a statistical question, compute the mean and median, measure the spread with range and MAD, then choose the best display and write an investigation report. Work through all four phases, fill every calculator, and complete the checklist.
A statistical question anticipates variability — different people, places, or times give different answers. Start your investigation by choosing a topic and a statistical question.
A statistical question has many possible answers — the data varies. Ask something like "How much ___ does each ___ have?" rather than "What is the total ___?" Make sure to name what you are measuring and who or what you are measuring it on.
Compute the mean and median for your selected dataset, then compare them. Are they close? What does that tell you about the shape of the distribution?
Mean: Add all values, divide by count. Sensitive to outliers.
Median: Sort values; take the middle (or average two middles). Resistant to outliers.
If mean > median, the data may be skewed right. If mean < median, it may be skewed left. If they are close, the data is roughly symmetric.
Compute the range and mean absolute deviation (MAD) to describe how consistent or spread out your data is. A small MAD means the data clusters near the mean.
Range = Maximum − Minimum.
MAD steps: (1) Find the mean. (2) Subtract the mean from each value, then take the absolute value. (3) Average all those absolute deviations.
Quick-check mean = (4 + 8 + 6 + 10 + 2) ÷ 5. Add them all up first!
Based on your data and its shape, choose the best type of display and the best measure of center. Justify your choices.
Display guide: Use a dot plot for small data sets (fewer than ~20 values). Use a histogram for large data sets grouped into intervals. Use a box plot to show the five-number summary and compare two groups.
Measure of center: If the mean and median are far apart, an outlier or skew is pulling the mean — in that case, the median is more representative. If they are close, the mean is fine.
Quick-check: When mean (14) and median (8) are far apart, the mean is pulled by high outliers. The median (8) is more resistant and better represents the typical value.
Write a 5–7 sentence investigation report. Include your statistical question, the mean and median, the range and MAD, your chosen display, the best measure of center, and what your findings mean in context.
| Category | 4 — Expert | 3 — Proficient | 2 — Developing |
|---|---|---|---|
| Statistical Question (6.SP.1) | Question clearly anticipates variability; units correctly identified; strong reasoning | Question is statistical; units identified | Question is partially statistical or units missing |
| Mean & Median (6.SP.3 / 6.SP.5c) | Both correct with work shown; comparison explains what the difference reveals about shape | Both correct; comparison attempted | One correct or minor computation error; comparison missing |
| Range & MAD (6.SP.5c) | Both correct with full steps shown; spread interpreted meaningfully in context | Both correct; interpretation attempted | Range correct; MAD has a step error; interpretation limited |
| Display & Best Measure (6.SP.4 / 6.SP.2) | Display and measure of center correctly chosen and well-justified based on data shape | Correct choices with some justification | Choices made but justification is missing or unclear |
| Communication (Investigation Report) | Report uses all five measures, explains findings in context, and draws a meaningful conclusion | Report uses most measures; conclusion present | Report is incomplete or context missing |