Blood group falls into four boxes with nothing in between. Height does not. That difference is not cosmetic — it tells you how many genes are involved, whether the environment has a say, and which statistics you are allowed to use on the data.
📘 What you need to know
Discrete (discontinuous) variation falls into clear-cut categories with no overlap and no in-between values. Blood group is the standard example.
Continuous variation occurs when two or more genes affect the characteristic, giving a range of values between two extremes.
Characteristics controlled by many genes are polygenic. Each allele has a small effect, and those effects add together.
Continuous data typically form a normal distribution — a bell-shaped curve.
Continuous characteristics are strongly influenced by the environment; discrete ones usually are not.
A box plot summarises data using five values: lowest, first quartile, median, third quartile and highest.
An outlier lies more than 1.5 × IQR above the third quartile or below the first quartile, and is plotted separately.
Two kinds of variation
Discrete variation means the characteristic falls into two or more distinct classes with nothing between them. Human blood is group O, A, B or AB, each with a Rhesus factor that is positive or negative, giving eight categories and no intermediates. You cannot be slightly group A.
Continuous variation means a range of values exists between two extremes, and any value in that range is possible. Height and mass are the obvious examples. There is no list of allowed heights.
The trap of grouped data. Shoe size looks discrete, because shoes come in whole and half sizes. But feet vary continuously; the sizes exist because manufacturers cannot make a bespoke shoe for everybody. When you are deciding which type of variation you are looking at, ask whether the underlying characteristic is continuous, not whether the recording method put it in boxes.
The shape of continuous data
Plot a continuous characteristic for a large population and you almost always get the same shape: most individuals near the middle, with numbers falling away symmetrically towards both extremes. That is a normal distribution.
The 5 cm groupings are a convenience for drawing, not a feature of the biology. That is the difference between this and a bar chart of blood groups, where the categories are real.
A quick test you can apply to any graph in an exam: are the bars touching? Continuous data are drawn as a histogram with bars touching, because the categories run into one another. Discrete data are drawn with gaps between the bars. That one visual detail often answers “what type of variation is shown”.
Why many genes produce a smooth range
Continuous variation arises when two or more genes affect the same characteristic. At the genetic level, different alleles at a single locus have only a small effect on the phenotype. Different genes can have the same effect, and those effects add together. When a large number of genes combine in this way they are called polygenes.
Human height is the classic case. It is influenced by bone length, skeletal muscle structure, how effectively food substances are absorbed and hormone production, each of which involves genes of its own. Add environmental factors — diet, exercise, prenatal nutrition, general lifestyle — and the result is a smooth range rather than a set of categories.
The rule for continuous traits
phenotype = genotype + environment
Skin colour works the same way. Several genes control the production of melanin, and the more melanin produced the darker the pigmentation. On top of that, exposure to ultraviolet light darkens skin further. Genotype sets a range; the environment decides the position within it.
Feature
Continuous variation
Discontinuous variation
Definition
Measurable across a complete range from one extreme to another; the data are quantitative
Falls into distinct classes; the data are qualitative or categorical
Number of gene loci
Many, often on different chromosomes
Usually one, sometimes a very small number
Number of alleles involved
Many pairs, since many genes contribute (polygenic)
Usually a single pair (monogenic)
Effect on phenotype
Many intermediate phenotypes between the extremes
The feature is either present or absent; differences are discrete
Environmental influence
Significant
Little or none
Examples
Height in humans, milk yield in cattle
Human blood group, ability to roll the tongue
Box and whisker plots
Once data are continuous you need a way to summarise them. A box plot splits the data into quartiles and shows what is happening at the low, middle and high points, together with any extreme values.
🧩 The five values you need
Lowest data value (excluding outliers)
First quartile — the value one quarter of the way through the ordered data
Median — the middle value. It will not necessarily sit in the middle of the box
Third quartile — three quarters of the way through
Highest data value (excluding outliers)
The middle three values form the box, whose width is the interquartile range — the middle 50 per cent of the data. The lowest and highest values are joined to the box by horizontal lines called whiskers, which represent the lowest 25 per cent and the highest 25 per cent.
Notice the median is not in the middle of the box. That asymmetry is information: it tells you the data are skewed, which a mean on its own would hide.
Outliers
Outliers are data points at the extremes, well above or below the rest. The convention is arithmetic rather than a matter of judgement: a value is an outlier if it lies more than 1.5 × the interquartile range above the third quartile or below the first quartile. Outliers are plotted separately from the whiskers, usually as a cross or a dot, so that they do not distort the picture of the bulk of the data.
Worked examples
WORKED EXAMPLE
For the leaf data above, Q1 = 38.5 mm and Q3 = 45.5 mm. Determine whether a leaf of length 27 mm would be classified as an outlier. [3]
Step 1: find the interquartile rangeIQR = 45.5 − 38.5 = 7 mmStep 2: find the lower limit1.5 × 7 = 10.5lower limit = Q1 − 10.5 = 38.5 − 10.5 = 28 mmStep 3: compare27 mm is below 28 mmYes — 27 mm is an outlier and would be plotted separatelyshow the limit itself, not just the verdict; the arithmetic is where the marks are
WORKED EXAMPLE
A student measures the mass of 200 birds of one species and plots a histogram with touching bars showing a bell-shaped distribution. Deduce the type of variation and explain what this suggests about the genes involved. [3]
Read the evidence from the graphthe bars touch and there are no distinct categories, only a range between two extremesName the typethis is continuous variation, shown by a normal distributionExplain the geneticsit must be polygenic: many genes each contribute a small additive effect, and the environment influences it too3 marks: continuous variation identified, evidence quoted, polygenic control explained“deduce” means the evidence from the graph must appear in your answer
💡 Exam tips
To classify variation from a graph, look for touching bars and no gaps (continuous) versus separate bars for named categories (discrete).
For continuous traits, always mention both polygenic control and environmental influence. Answers giving only one rarely get full marks.
Learn the outlier rule as a calculation: find the IQR, multiply by 1.5, add to Q3 or subtract from Q1.
Remember the median need not be central within the box, and say what that tells you if asked to interpret.
The whiskers stop at the most extreme values that are not outliers. Do not stretch them out to reach an outlier.
⚠️ Common mix-ups
Calling shoe size discrete variation. The recording is grouped; the underlying characteristic is continuous.
Saying continuous variation is “caused by the environment”. It is caused by many genes; the environment modifies it.
Confusing range with interquartile range. Range is highest minus lowest; IQR is Q3 minus Q1, the middle half only.
Assuming the median is the mean. A box plot shows no mean at all.
Including outliers inside the whiskers. They are plotted as separate points, outside the whisker ends.
Treating a bell shape as proof of a single gene. The bell shape is a signature of many genes acting together.
Up next: Evolution & Natural Selection — all this variation finally does something, as the environment starts selecting between the phenotypes it has produced.
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