Continuous variation and box-and-whisker plots

Organisms (Continuity and change) · Inheritance · note 7 of 10

Spec D3.2.14, D3.2.15Download all Inheritance notes (PDF)Download all notes (PDF)13 pages

Continuous variation and box-and-whisker plotsSpec D3.2.14, D3.2.15

In short

Continuous variation is variation in which a trait can take any value in a range, due to polygenic inheritance and/or environmental factors, such as skin colour or height. Discrete variables, such as ABO blood group, fall into separate classes. A box-and-whisker plot shows a continuous variable's minimum, quartiles, median, maximum and outliers.

Polygenic inheritance is the control of one trait by many genes, each with a small additive effect. With many genes the number of possible genotypes is large, so phenotypes form a continuous range, usually close to a normal distribution. Environmental factors add further variation.

Skin colour in humans is polygenic: several genes affect the amount and type of melanin. Environment also matters, because exposure to sunlight increases melanin production.
A continuous variable, such as skin colour or height, can take any value in a range.
A discrete variable, such as ABO blood group, falls into distinct categories with no intermediates.

Mean: The sum of all values divided by the number of values.
Median: The middle value when the data are in order.
Mode: The most frequent value (or class).

Box-and-whisker plots

A box-and-whisker plot displays six aspects of a data set: outliers, minimum, first quartile (Q1), median, third quartile (Q3) and maximum. The box runs from Q1 to Q3 with a line at the median. The whiskers reach the lowest and highest values that are not outliers.

interquartile range (IQR) = Q3 − Q1; outlier if > Q3 + 1.5 × IQR or < Q1 − 1.5 × IQR

Outliers in student height data

Heights of a class of students (cm): Q1 = 160, median = 166, Q3 = 172. The shortest student is 145 cm and the tallest is 191 cm. Determine whether either is an outlier.

IQR = 172 − 160 = 12 cm.
1.5 × IQR = 18 cm.
Upper limit = 172 + 18 = 190 cm. Lower limit = 160 − 18 = 142 cm.
191 cm > 190 cm, so it is an outlier. 145 cm > 142 cm, so it is not.

Answer: 191 cm is an outlier (plotted as a separate point); the upper whisker ends at the tallest non-outlier. 145 cm is the minimum.

Box-and-whisker plot of student height in cm from 140 to 195: minimum 145, Q1 160, median 166, Q3 172, an upper whisker to the tallest non-outlier, and a separate point at 191 labelled outlier, greater than Q3 + 1.5 × IQR. — The six aspects of a box-and-whisker plot, using the student height data from the worked example. 191 cm is beyond 190 cm (Q3 + 1.5 × IQR), so it is plotted as an outlier.

Maths skill:

Box plots let you compare two samples quickly: compare medians for the typical value and IQRs for spread. State the units every time.

Exam tip:

Linking question: what are the principles of effective sampling in biological research? A larger random sample gives quartiles and medians that better represent the population.

Written and checked against the IB Biology HL specification · Updated October 2026

Frequently asked questions

What is the difference between genotype and phenotype?

Genotype is the combination of alleles an organism inherits, for example Aa. Phenotype is the observable traits of the organism, which result from its genotype and environmental factors. Some traits depend on genotype only, such as ABO blood group; others, such as height, depend on genes interacting with the environment.

What is the difference between codominance and incomplete dominance?

In codominance the heterozygote has a dual phenotype, with both alleles fully expressed, as in blood group AB with A and B antigens. In incomplete dominance the heterozygote has an intermediate phenotype, as in pink four o'clock flowers from red and white parents. Both give a 1:2:1 phenotype ratio in the F2.

Why are sex-linked disorders more common in males?

Sex-linked disorders such as haemophilia are caused by recessive alleles on the X chromosome. Males have only one X chromosome, so a single recessive allele is expressed. Females have two X chromosomes and are affected only if both carry the recessive allele, so they are usually unaffected carriers.

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