Success criteria
- I keep fractional measurements exact on a line plot.
- I calculate minimum, maximum, mean, median, mode, and range and explain what each reveals.
- I describe a line graph with values and intervals, not only “up” or “down.”
- I choose a representation that matches the type of data and question.
Learn and explain
The plot preserves quarters: 1.25 m occurs 3 times; 1.5 m occurs 2 times; 1.75 m occurs 1 time. Their combined length is 8.5 metres.
A line plot shows the distribution of separate measurements. A line graph connects values recorded in order—often over time—to show change.
| Day | Mon | Tue | Wed | Thu |
|---|---|---|---|---|
| Pages read | 18 | 21 | 20 | 27 |
Explain: Which representation would you use to show shoe sizes in a class? Which would you use for temperature each hour? Why?
Six landmarks, six different questions
For the ordered data 3, 5, 5, 7, 8, 8, 8, 12:
| Landmark | Value | What it tells us |
|---|---|---|
| Minimum | 3 | smallest observation |
| Maximum | 12 | largest observation |
| Mean | 7 | equal-share average |
| Median | 7.5 | middle after ordering |
| Mode | 8 | most frequent value |
| Range | 9 | maximum minus minimum |
No landmark is automatically “best.” Choose the one that answers the question, and compare more than one when a single summary hides the shape of the data.
Independent practice
Across the reading week, how many more pages were read on Thursday than Monday?
The change from first to last is 9 pages.
During which interval was the largest increase?
Wed to Thu increased by 7 pages.
What is the mean of 3, 5, 5, 7, 8, 8, 8, 12?
The total shared equally across all observations is 7.
What is the range of 3, 5, 5, 7, 8, 8, 8, 12?
12 − 3 = 9.
Which value is the mode of the landmark dataset?
8 occurs most often.
Unfamiliar transfer — authentic data (offline first)
Collect 8–12 measurements from an authentic activity: model-piece lengths, rainfall, ingredient masses, or practice times. Graph them by hand first. Calculate all six landmarks, write two observations, and explain which landmark is most useful for one real question.
Delayed check
One week later, choose between a line plot, line graph, or bar graph for three new datasets. Defend each choice before drawing anything, then calculate the six landmarks for one dataset and check them from the ordered values.
Evidence path
Save the hand-drawn graph, raw data table, and explanation to jeremy/portfolio/math/unit-6/lesson-17-represent-data/.
Next step
- Repair: if fractional positions drift, rebuild the axis with equal quarter intervals.
- Continue: if graph choice and all six landmarks are secure, use data and probability to test a claim.
- Stretch: compare two datasets that have the same mean but different ranges and distributions.