3.2 Tables, Trends & Patterns

3.2 Tables, Trends & Patterns

Tables are the most honest display in science: every value is written down exactly, with nothing stretched or squashed to fool your eye. But ICAS still finds ways to test you — by hiding the cell you need among lookalike cells, by asking what the whole pattern means, or by asking you to estimate a value that was never recorded. This section gives you a routine for all of it.

Reading a Table Properly

Before reading a single number, read the title or caption, then every row heading and column heading, including the units. Units live in the headings, not in the cells, so a bare "35" means nothing until you know it is 35 seconds.

Here are two tables in the style ICAS uses. The first tracks one changing variable; the second is a two-way table comparing locations across several measures.

A scientist timed how long one sugar cube took to dissolve in water at different temperatures:

Finding the Exact Cell

Use the two-finger method: one finger on the row heading, one on the column heading, and slide them to the intersection. What is the inland town's July temperature? Row "Inland town", column "Average July temperature (°C)" — 12 °C. ICAS distractors are usually the neighbouring cells: 33 °C (the same row, wrong column), 17 °C (the same column, wrong row). Slow down, trace both headings, and say the units to yourself.

Spotting Trends

A trend is the direction the numbers move as one variable changes. Learn the sentence frames and you can answer most trend questions in one line:

• As X increases, Y increases.
• As X increases, Y decreases.
• As X increases, Y stays the same or levels off.

In the sugar table, as the water temperature increases, the dissolving time decreases. Look closer and there is more to say: the drops are 13, 9 and 6 seconds, so the time is falling by smaller and smaller amounts — the trend is levelling off. Trends are not always straight lines, and noticing how a trend changes earns the harder marks. In the climate table there is a pattern across columns: the inland town is hotter in January, colder in July and far drier — a bigger temperature range and lower rainfall than the coast.

Patterns vs One-Off Anomalies

An anomaly (also called an outlier) is a value that breaks the pattern. If the dissolving time at 40 °C had been 50 seconds instead of 26, that cell would stick out from the smooth decrease. What should a scientist do? Check the equipment, repeat that measurement, and keep the repeated result if it agrees with the trend — but never silently delete an odd value just because it looks wrong. One anomaly does not destroy a trend; the trend is what the majority of points are doing.

Interpolation vs Extrapolation

Interpolation means estimating a value between two recorded values. At 35 °C — halfway between the 30 °C and 40 °C rows — the dissolving time should sit between 35 and 26 seconds, so about 30 seconds is a sensible estimate. Because it sits inside a smooth, measured trend, interpolation is reasonably safe.

Extrapolation means extending the pattern beyond the recorded data — predicting the time at 70 °C, or at 5 °C. This is risky, because patterns change outside the range you measured. Water near 0 °C freezes, so the dissolving trend cannot simply continue downwards; at very high temperatures the water itself is close to boiling and the whole set-up changes. ICAS regularly offers an extrapolated answer that assumes the trend runs forever — treat those options with suspicion unless the science supports them.

Turning an Experiment into a Table

Some ICAS questions describe an experiment in words and ask which table would record its results. The recipe: the independent variable (what was changed on purpose) becomes the first column; the dependent variable (what was measured) becomes the next column; repeated trials become extra rows or columns. Variables that were kept the same (controlled) do not get columns — they belong in the caption. If Mia drops a ball from 50, 100, 150 and 200 cm and measures the bounce height three times at each height, the table needs drop height in the first column and bounce heights in the next three, with units in the headings. Any option missing the independent variable, or giving a column to something held constant, is wrong.

Matching a Table to a Graph

A classic ICAS move shows a table and four candidate graphs. Work through three checks, in this order:

1. Labels and units — does each axis show the right variable with the right unit? This alone usually eliminates one or two options.
2. Exact points — pick two or three cells from the table and check they are plotted where they should be. A graph can have the right labels but wrong points.
3. Overall shape — rising, falling or levelling? The shape must match the trend in the numbers.

Never match on shape alone. "It goes down" fits a hundred wrong graphs; the axes and the exact points are what make one graph correct.