Describe an association from a scatterplot

As length increases, what generally happens to mass in this sample?

How would you describe the direction of this charge pattern?

Predict the direction when the change per x unit is negative, zero and positive. Try −8, 0 and +8. The axes stay fixed and the points are not joined

What happens at zero change?

Two plots use identical axes. In both, all points lie exactly along an increasing straight pattern, but one is steeper. Which conclusion is justified?

Predict how increasing scatter size changes the pattern. Compare 0, 6 and 12. The dashed line is the fixed underlying model, not a line joining observations. Both axis scales stay fixed

What does increasing this scatter size do?

Which description fits this plotted pattern?

What can be said about this cloud?

In this plot, U lies well above the main increasing pattern. What is the appropriate first response?

Which report best describes these clay samples?

A cloud appears to have two separate groups. What should an investigation check?

Changing the vertical unit from grams to kilograms makes a graph look flatter if the same numerical tick spacing is retained. Does this alone weaken the association?

Plan a small bivariate investigation

Use the four synthetic clay samples A (2 cm,18 g), B (4 cm,32 g), C (5 cm,28 g) and D (7 cm,54 g). Ask whether mass tends to increase with length, plot them and write a cautious report

1. 1Report There is a generally increasing pattern, but the sample is small and C is lighter than B despite being longer. Do not claim an exact rule or causation
2. 2Improve the evidence Plan more samples with a stated selection method. Record thickness and material if relevant. Identify the data source and any missing observations
3. 3Ethics and review Use synthetic or appropriately permitted non-identifying data. Review your drawing and report yourself or with a teacher; this task is not automatically marked

Construct and compare four numerical patterns

Four original fictional profiles share x values 1, 2, 3, 4, 5, 6, 7. Their y values are A: 12, 18, 24, 30, 36, 42, 48; B: 12, 25, 34, 40, 44, 46, 47; C: 30, 14, 46, 30, 46, 14, 30; and D: 48, 42, 36, 30, 24, 18, 12. Draw each with a horizontal axis from 0 to 8 and a vertical axis from 0 to 70. Preserve the given pairing and do not join points

1. 1Describe and justify Write a separate account of direction, form and clustering for each. Use coordinate evidence rather than apparent steepness. Explain why no clear overall directional tendency does not prove no possible relationship. For A, convert every y value to thousands of units and explain the effect of changing the vertical scale
2. 2Investigate an unusual observation In a separate copy of A, replace (4,30) with (4,60). Identify the unusual observation relative to the other six points. Compare the full and reduced displays, retain the original record, and explain what evidence would be needed before correcting or excluding it. No formal outlier rule or cause is supplied
3. 3Choose and verify technology Choose an XY plotting tool and record the paired columns, common windows and point-only settings. Verify all seven points per panel, then list successive y changes for A, B and D. Check that your description accounts for the whole pattern, not merely the first and last point
4. 4Complete before continuing Review your labelled plots, written report and technology record yourself or with a teacher

Model response: direction, form and strength are separate

The profiles share x values 1, 2, 3, 4, 5, 6, 7. Their y values are A: 12, 18, 24, 30, 36, 42, 48; B: 12, 25, 34, 40, 44, 46, 47; C: 30, 14, 46, 30, 46, 14, 30; and D: 48, 42, 36, 30, 24, 18, 12. A lies exactly on an increasing straight pattern: its y increases by 6 for every x step, so it is a perfect positive linear association in these supplied values. D has changes of −6 and is a perfect negative linear association. B increases but levels off: successive changes are 13,9,6,4,2,1, supporting a clear positive non-linear pattern rather than a constant-rate straight line

1. 1Account for all points C has values above, below and equal to 30 and is symmetric about the x value 4; it has no clear overall increasing or decreasing tendency. Equal endpoints alone would not establish that: inspect all seven points. This description does not prove population independence or rule out every structured relationship. Strength/form words here are descriptive; no universal numerical cutoff is being applied
2. 2Rescaling and unusual cases A in thousands has y values 0.012,0.018,0.024,0.030,0.036,0.042,0.048. The points remain exactly linear despite altered numerical slope. In the separate modified A, the point with x value 4 and y value 60 is 30 units above the continuation of the other six points, which has y value 30 at that x value. Investigate whether it is a transcription error, unusual condition or genuine observation; the display alone does not justify deletion. Report any with/without comparison and its reason
3. 3One reproducible workflow Use an X column 1–7 and four labelled Y columns. Make four XY point plots with identical windows and tick scales. Verify seven records per profile against the supplied lists. Calculate successive Y differences to check constant change in A/D and changing increments in B. Save the original A column before making the one-point variant; never silently overwrite evidence. Record the new y unit explicitly when rescaling

All A points lie exactly on the increasing straight pattern. Does changing y from units to thousands of units weaken this pattern?

Which account includes the whole B profile?

What does C support about its overall direction?

Which description fits D on these fixed axes?