lesson
Keep each pair together
1 · Learn
Each point on a scatter graph contains TWO measurements for the same case. The fictional daily pairs (temperature in °C, drinks sold) are (10,19), (12,25), (14,26), (16,34), (18,35), (20,41). Put temperature on the horizontal axis and drinks sold on the vertical axis. Do not sort the two lists independently: that would destroy the pairing.
The supplied scatter graph shows a positive association: higher temperatures tend to accompany more sales in these six records. Do not join the points in temperature order as though they describe a single continuous journey. Scatter describes paired observations, not a line through every point.
The dashed line y = 2x is a reasonable ROUGH summary for these particular points, with small deviations on both sides. A hand-drawn line of best fit is not unique. It should follow the overall pattern, need not pass through any particular point, and must not be forced through the origin. At x = 15, the line estimates about 30 sales.
Fifteen degrees is inside the observed range 10–20°C, so that estimate is interpolation. A prediction at 30°C is extrapolation and may be unreliable. Neither is a promise for an individual day. This observational association does not prove temperature caused the sales: other influences, including opening hours or the number of visitors, may differ too. The data is invented for graph practice, not scientific evidence.
A SECOND fictional dataset has pairs (10,41), (12,35), (14,34), (16,26), (18,25), (20,19). Its graph shows negative association: sales tend to be lower at higher temperatures in these invented records. The rough line y = 60 - 2x estimates 30 sales at 15°C. Negative describes the direction of a relationship, not a negative sales count. It still does not prove cause. If points show no clear pattern, report no clear association in that sample rather than inventing a trend.
2 · Worked example
The point (14,26) sits below the rough line because y=2×14 predicts 28. The difference is 26-28=-2 sales. A point does not become wrong merely because it is not exactly on the line; check measurement and context before removing any observation.
3 · Your turn
Using the rough line, estimate sales at 17°C and at 25°C. Which is interpolation? Does the graph establish that every 2°C rise causes exactly four extra sales?
Check your answer
About 34 and 50 sales. Seventeen degrees is interpolation; 25 is extrapolation beyond the observed range. No: the points vary, the line is only a rough summary, and this small observational dataset does not establish that causal rule.
4 · Apply your learning
Plot the six supplied pairs on squared paper, keeping each temperature with its sales count. Draw a reasonable trend line and compare two predictions with a partner. Explain any small difference in your estimates using the line placement rather than declaring one unsupported exact answer.
Adult guidance and safety
Use the supplied fictional datasets, not pupil personal records. Check frequency totals, axis scales, keys and denominators. Provide squared paper, a ruler and protractor. A chart supports an interpretation only within the dataset and collection method stated.
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