4.8.6Additional lessons
Continuous Variation: Skills — IB Biology HL Revision Notes & Topical Questions
5 min read 5 parts Lesson 73 of 101
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Section 1 of 5Types of Variation
Discrete variation
- Discrete variation Individuals fall into clear categories with no intermediates, as with ABO blood groups, controlled by one gene with few alleles.
Continuous variation
- Continuous variation Individuals show a full range of values between two extremes, such as height, mass or leaf length.
Polygenic control
- Polygenic control Continuous traits are controlled by many genes, each adding a small effect to the phenotype.
Environmental effect
- Environmental effect Diet, exercise, light and temperature also change the phenotype, which smooths the differences between individuals.
Distribution
- Distribution Plotted as a histogram, continuous data often form a bell-shaped normal distribution around the mean.
| Feature | Discrete | Continuous |
|---|---|---|
| Genes involved | One or few | Many (polygenic) |
| Environment | Little effect | Large effect |
| Data type | Categories | Measurements in a range |
| Example | Blood group | Height |
Section 2 of 5Box-and-Whisker Plots
Box-and-Whisker Plots
Purpose
- Purpose A box plot shows the spread and centre of a data set, and is useful for comparing two or more groups side by side.
Five values
- Five values The minimum, lower quartile (Q1), median, upper quartile (Q3) and maximum are marked on a scale.
Box
- Box The box runs from Q1 to Q3 and holds the middle 50% of the data;
- its length is the interquartile range, IQR = Q3 − Q1.
Whiskers
- Whiskers Lines extend from the box to the smallest and largest values that are not outliers.
Outliers
- Outliers A value more than 1.5 × IQR above Q3 or below Q1 is plotted as a separate point and treated as an outlier.
Section 3 of 5Building a Box Plot
Follow the same order of steps each time you draw one.
1
Arrange the data in order from the smallest value to the largest value so that the middle values are easy to find.
2
Find the median, which splits the ordered data into a lower half and an upper half of equal size.
3
Find the median of the lower half to give Q1 and the median of the upper half to give Q3, then calculate the IQR.
4
Calculate the outlier limits at Q1 − 1.5 × IQR and Q3 + 1.5 × IQR and mark any values beyond them as separate points.
5
Draw the box and median line on an evenly scaled axis, extend the whiskers to the extreme non-outlier values, and label the axis with units.
Section 4 of 5Worked Example
Question
- Ten plants have heights in cm: 41, 43, 44, 46, 47, 48, 50, 52, 53, 70.
- Find the median, quartiles and IQR, and decide whether 70 is an outlier.
- Medianthe middle lies between 47 and 48, so the median = 47.5 cm.
- Lower half is 41 to 47, so Q1 = 44 cm; upper half is 48 to 70, so Q3 = 52 cm.
- IQR = 52 − 44 = 8 cm.
- Upper limit = Q3 + 1.5 × IQR = 52 + 12 = 64 cm; 70 is above this limit.
Answer
- Median 47.5 cm, Q1 44 cm, Q3 52 cm, IQR 8 cm;
- 70 cm is an outlier and is drawn as a separate point.
Section 5 of 5Exam Checklist & Tips
4.8.6 – Key Points for the Exam
- Continuous variation Variation in which values form an unbroken range between extremes.
- Polygenic Controlled by the combined effect of many genes.
- Interquartile range The difference between the upper and lower quartile, covering the middle half of the data.
- Outlier A value far enough from the rest to be plotted separately, beyond 1.5 × IQR from the box.
Common Mistakes
- Saying that continuous traits are controlled by one gene.
- Ignoring the environment when explaining why height varies.
- Drawing the whiskers to the outlier instead of to the largest non-outlier value.
- Using the range, rather than the IQR, to describe the middle spread of the data.
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