Analysing and Evaluating Data » Presenting and Processing Data

Tables and frequency tables

Once you have collected data, you must present it clearly so that patterns can be seen. The first step is a results table. Put the independent variable in the first column and the dependent variable next to it. Every column heading needs its unit, for example Temperature (°C). Units go in the heading, not in every cell.

Sometimes you count how often each value turns up. A frequency table does this. Imagine you count the seeds in 20 pea pods:

• 3 seeds: 2 pods
• 4 seeds: 5 pods
• 5 seeds: 8 pods
• 6 seeds: 4 pods
• 7 seeds: 1 pod

The frequencies add up to 20, the number of pods. Always check that your total matches the number of things you counted.

Key terms:

• Frequency: how many times a value, or a value in a group, occurs.
• Distribution: the way the results are spread out, from the lowest to the highest value.

Choosing the right graph

The kind of data decides the kind of graph. Pick the wrong one and the picture can mislead.

Plotting a line graph, step by step:

1. Put the independent variable on the x-axis and the dependent variable on the y-axis.
2. Choose scales that use more than half of the grid. Use equal steps, such as 2, 4, 6, 8.
3. Label each axis with its quantity and unit.
4. Plot each point as a small neat cross.
5. Draw a smooth line of best fit through the points. Do not join them dot to dot unless told to.

A histogram also shows the distribution of your results.

Translating data and reading graphs

You must be able to move data from one form to another. A table of numbers becomes a graph when you plot it. A graph becomes numbers when you read values off it. To read a value, go across from the y-axis or up from the x-axis until you meet the line, then read the other axis.

A straight-line graph gives two useful numbers.

• Slope (gradient): change in y divided by change in x. It tells you the rate of change.
• Intercept: where the line crosses the y-axis.

Many biology graphs are curves. The rate at one moment is found by drawing a tangent, a straight line that just touches the curve at that point. Then work out the slope of the tangent. If the tangent rises 12 cm³ over 6 minutes, the rate at that point is 12 ÷ 6 = 2 cm³ per minute.

The area between a curve and the x-axis also has a meaning. On a graph of rate against time, the area is the total amount made. Count the squares under the curve, then multiply by what one square is worth. If each square stands for 1 cm³ and you count 12 squares, the total is 12 cm³. Count part squares as halves when they are about half covered.

Calculations with data

You already know how to find a percentage change and a rate from earlier lessons. Here are the other skills the spec asks for.

• Arithmetic mean: add up all the values and divide by how many there are.
• Range: the highest value minus the lowest value, or written as "from lowest to highest".

Changing the subject of an equation. Rate = change ÷ time. To find the change, rearrange to change = rate × time. Substitute the numbers and keep the units. A rate of 0.5 cm³ per minute for 8 minutes gives 0.5 × 8 = 4 cm³.

Order of magnitude. Remember from the lesson on eukaryotes and prokaryotes that this is a power of ten. A value 1,000 times bigger is three orders of magnitude bigger.

Significant figures. Round your answer to the same number of significant figures as the least precise data you used. A mean of 3.4666 from data given to two significant figures is written as 3.5. How to count significant figures is covered in Units, Prefixes and Significant Figures.

Spread and uncertainty

Whenever you make a measurement, there is always some uncertainty about the result you get. Repeat the measurement and you will probably get slightly different answers. The range of a set of repeats, taken about the mean, is a measure of that uncertainty.

In the leaf example the mean is 50 mm and the values run from 46 to 54 mm. Each result is within 4 mm of the mean, so the result can be written as 50 mm ± 4 mm. Uncertainty is half the range, so a range of 8 mm gives ± 4 mm. If the results are not balanced around the mean, use the biggest distance from the mean. The smaller the range, the smaller the uncertainty and the more you can trust the mean.

Key terms:

• Uncertainty: the amount by which a measurement could be wrong, shown by the spread of repeat results.
• Tangent: a straight line that touches a curve at one point, used to find the rate of change there.

Exam-style question

A student measured the length of five seedlings grown in the light. The lengths in mm were: 35, 41, 38, 40, 36.

(a) Calculate the mean length of the seedlings. [2 marks]

(b) Give the range of the results. [1 mark]

(c) The student repeats the experiment for 2, 4, 6, 8 and 10 days and plots mean length against the number of days. Which variable goes on the x-axis, and why is a line graph better than a bar chart? [2 marks]