Calculate the standard deviation of the stomatal counts 12, 15, 14, 10 and 9.

The mean is 12 and the squared deviations are 0, 9, 4, 4 and 9, totalling 26. σ̂ = √(26 ÷ (n − 1)) = √(26 ÷ 4) = 2.55.

What is the standard error of the mean, and how is it calculated?

It estimates how closely the sample mean is likely to match the true population mean, and equals the standard deviation divided by the square root of the sample size, σ̂/√n.

Calculate the standard error and 95% confidence limits for a mean of 12 with σ̂ = 2.55 and n = 5 (t = 2.78 for 4 degrees of freedom).

SE = 2.55 ÷ √5 = 1.14. The 95% confidence limits are 12 ± 2.78 × 1.14, that is 12 ± 3.2, from 8.8 to 15.2.

When is Student's t-test used, and what are its degrees of freedom?

To test whether the means of two independent samples of normally distributed, continuous data differ significantly; the degrees of freedom are n₁ + n₂ − 2.

CCEA A-Level Biology 1010

Biological Molecules

Topic overview Water as a solvent Inorganic ions and their roles Monosaccharides and the glycosidic bond Disaccharides and polysaccharides Lipids, triglycerides and phospholipids Amino acids and protein structure Protein shape, conjugated proteins and prions Nucleic acids: nucleotides, DNA and RNA DNA replication and the Meselson–Stahl experiment Biochemical tests and paper chromatography

Enzymes

Topic overview Enzymes as globular proteins and the active site Specificity, cofactors and coenzymes Activation energy and models of enzyme action The effect of temperature and pH The effect of substrate and enzyme concentration Competitive and non-competitive inhibition Enzymes as biomarkers of disease and inhibitors as drugs Immobilised enzymes and biosensors

Viruses and Cell Structure

Topic overview Bacteriophage and HIV structure Viral replication in host cells Prokaryotic and eukaryotic cells compared Membrane structure: the fluid mosaic model Functions of membrane components Mitochondria and chloroplasts Ribosomes, endoplasmic reticulum, Golgi apparatus and lysosomes The nucleus, the cytoskeleton and plasmodesmata Plant, fungal and animal cells Microscopy, cell measurement and cell fractionation

Cell Physiology and Transport

Topic overview Diffusion and facilitated diffusion Membrane permeability Osmosis and water potential Plant and animal cells in different solutions Calculating the water potential of a cell Active transport, endocytosis and exocytosis Measuring water potential and solute potential in plant tissue

Continuity of Cells

Topic overview The cell cycle: interphase and the gap phases Control points in the cell cycle and cancer Chromosome structure, haploidy and diploidy Mitosis: the events of the four stages Cytokinesis and the significance of mitosis Anticancer drugs and the cell cycle Meiosis I and the first division Meiosis II and the significance of meiosis Preparing and examining slides of cell division

Tissues and Organs

Topic overview Tissues and organs The tissue layers of the ileum The mucosa, villi and crypts of Lieberkühn Adaptations of the ileum for absorption The mesophytic leaf and its epidermal layers Palisade and spongy mesophyll Leaf vascular tissue and stomata

Exchange Surfaces and Gas Exchange

Topic overview Surface area, volume and the surface area to volume ratio Features of efficient exchange surfaces The need for mass transport systems Fick's law and the rate of gas exchange Gas exchange in plants and the compensation point Gas exchange at the alveolus The respiratory tree and the mechanism of ventilation The effects of smoking on the breathing system Using a respirometer to measure gas exchange

Transport in Plants

Topic overview Epidermis, endodermis and the tissues of the root Xylem vessels and their lignification patterns Phloem: sieve-tube elements and companion cells Water and mineral ion uptake by root hairs The apoplast and symplast pathways Transpiration and the factors affecting its rate Cohesion-tension theory and the transpiration stream Translocation of organic solutes in the phloem Xerophytes and hydrophytes

The Circulatory System in Mammals

Topic overview Double circulation and the major blood vessels The structure and function of arteries, veins and capillaries Atherosclerosis, atheroma and the investigation of blood vessels The structure of the mammalian heart The cardiac cycle and the operation of the valves Myogenic stimulation and the electrocardiogram Blood cells and the stained blood film Plasma, tissue fluid and blood clotting Haemoglobin and the oxygen dissociation curve The Bohr effect, myoglobin and altitude

Adaptation and Biodiversity

Topic overview Adaptation and the ways organisms meet environmental challenges Ecological factors and the ecological niche Sampling procedures and sampling devices Estimating abundance, density, frequency and percentage cover The biochemical basis of life and the levels of biodiversity Measuring species diversity with Simpson's index Handling data: averages, spread and the t-test Taxonomy, nomenclature and the binomial system The concept of a species The taxonomic hierarchy from genus to kingdom Phylogenetic taxonomy and molecular evidence The five kingdom system: prokaryotae, protoctista and fungi Plantae, animalia and alternative classification systems

Human Impact on Biodiversity

Topic overview Monoculture, polyculture and intensive agriculture Crop rotation and hedgerow conservation Predator strips, pesticides and integrated pest management Organic pollution of waterways by slurry and silage effluent Eutrophication and fertiliser run-off Biological oxygen demand and reducing aquatic pollution Conservation initiatives and habitat protection Global warming, climate change and biodiversity

Homeostasis and Excretion

Topic overview Principles of homeostasis and negative feedback Excretion, osmoregulation and nitrogenous waste Gross structure of the kidney and the urinary system Structure of the nephron and its blood supply Epithelia of the nephron and their adaptations The glomerular filter Ultrafiltration and the forces that drive it Selective reabsorption in the proximal convoluted tubule The loop of Henlé and the medullary salt gradient ADH, osmoreceptors and the control of water balance

Immunity

Topic overview Natural barriers to infection Antigens, antibodies and the antigen–antibody reaction Antibody-mediated immunity and B-lymphocytes Cell-mediated immunity and T-lymphocytes Active immunity, passive immunity and vaccination Transplant rejection and immunosuppression Blood group polymorphism and the rhesus factor Transfusion compatibility and its consequences Antibiotic resistance and the search for new antimicrobials ELISA and the detection of disease biomarkers

Co-Ordination and Control

Topic overview Phytochromes and the control of flowering Plant growth substances and stem elongation The structure of a neurone Resting potential, threshold and the action potential Impulse propagation and the speed of conduction Synapse structure and chemical transmission Excitatory and inhibitory post-synaptic potentials Gross structure of the eye and accommodation The retina, rods and cones Skeletal muscle and the sliding filament theory

Populations and Communities

Topic overview Population growth curves, carrying capacity and environmental resistance r-selected and K-selected species Interactions between populations Biological control of pest species Population dynamics and changes in population size Estimating population size in the field and the laboratory Communities and ecosystems Succession and climax communities

Ecological Energetics and Nutrient Cycling

Topic overview Food chains, food webs and detritus food chains Trophic levels, gross and net primary production Ecological pyramids and their usefulness Energy transfer efficiency between trophic levels Why energy is lost at each trophic level Implications for agriculture and intensive farming The carbon cycle The nitrogen cycle and the role of bacteria

Respiration

Topic overview ATP and the ATP/ADP cycle Glycolysis The mitochondrion and the sites of aerobic respiration The link reaction and the Krebs cycle The electron transport chain and oxidative phosphorylation ATP yield from one molecule of glucose Anaerobic respiration in animals, plants and fungi Aerobic and anaerobic respiration compared, and oxygen debt Respiratory quotient and measuring respiration

Photosynthesis

Topic overview Chloroplast structure and the sites of photosynthesis Photosynthetic pigments and paper chromatography Absorption spectra and action spectra Photosystems, photoactivation and the Z-scheme Photolysis of water, reduced NADP and redox indicators Carbon dioxide fixation and rubisco Reduction of glycerate phosphate and regeneration of ribulose bisphosphate Limiting factors, the compensation point and measuring photosynthesis

DNA as the Genetic Code

Topic overview Genes and the nature of the genetic code Exons, introns and RNA splicing Comparing DNA and RNA Transcription and RNA polymerase Transfer RNA, ribosomes and the sites of translation Translation and polypeptide synthesis One gene, one polypeptide and the control of the phenotype Epigenetics, methylation and histone modification

Gene Technology

Topic overview The polymerase chain reaction DNA probes and genetic markers Microarrays, pharmacogenetics and personalised medicine Genetic fingerprinting and gel electrophoresis The stages of gene transfer Genetically modified microorganisms Transgenic animals and plants Gene therapy Genome sequencing and the Human Genome Project Gene inactivation and knockout organisms Social, ethical and ecological issues of gene technology

Genes and Patterns of Inheritance

Topic overview Genotype, phenotype and the environment Chromosomes, genes and alleles Monohybrid inheritance and Mendel's first law Codominance, multiple alleles and lethal alleles Test crosses Dihybrid inheritance and Mendel's second law Autosomes, sex chromosomes and sex determination Gene interaction and epistasis Polygenic inheritance and continuous variation The chi-squared test

Population Genetics and Evolution

Topic overview The gene pool The Hardy–Weinberg equation The Hardy–Weinberg principle and its conditions Sources of genetic variation Fitness and the process of selection Stabilising and directional selection Species and speciation Evidence and argument in evolutionary biology

Evolutionary Trends in Plants

Topic overview Colonising the land: the problems to be solved The moss body plan The fern body plan The flowering plant body plan Comparing the three plant groups Practical study of plant specimens Where each group can live, and why

Evolutionary Trends in Animals

Topic overview Body plans and the features compared Phylum Cnidaria Phylum Platyhelminthes Phylum Annelida Phylum Arthropoda Phylum Chordata Comparing the five phyla Practical study of animal specimens

Adaptation and Biodiversity

Handling data: averages, spread and the t-test

3 things to know
Unit AS 2

Overview

Mean, median and mode, standard deviation, standard error and 95% confidence limits, a worked t-test on stomatal counts, correlation and causation, presenting tables and graphs, and writing a bibliography.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What are the mean, median and mode of a data set?

Process

How are 95% confidence limits interpreted when two means are compared?

Key term

What are the median and the mode?

Questions from this subtopic

Each one with the model answer underneath.

1
What are the mean, median and mode of a data set?
Model answer
The mean is the sum of the values divided by their number, the median is the middle value when they are ranked, and the mode is the most frequent value; the median is least affected by outliers.
2
Calculate the standard deviation of the stomatal counts 12, 15, 14, 10 and 9.
Model answer
The mean is 12 and the squared deviations are 0, 9, 4, 4 and 9, totalling 26. σ̂ = √(26 ÷ (n − 1)) = √(26 ÷ 4) = 2.55.
3
What is the standard error of the mean, and how is it calculated?
Model answer
It estimates how closely the sample mean is likely to match the true population mean, and equals the standard deviation divided by the square root of the sample size, σ̂/√n.
4
Calculate the standard error and 95% confidence limits for a mean of 12 with σ̂ = 2.55 and n = 5 (t = 2.78 for 4 degrees of freedom).
Model answer
SE = 2.55 ÷ √5 = 1.14. The 95% confidence limits are 12 ± 2.78 × 1.14, that is 12 ± 3.2, from 8.8 to 15.2.
5
How are 95% confidence limits interpreted when two means are compared?
Model answer
If the confidence intervals of two means do not overlap, the difference between them is likely to be significant; if they overlap widely, it probably is not.
6
When is Student's t-test used, and what are its degrees of freedom?
Model answer
To test whether the means of two independent samples of normally distributed, continuous data differ significantly; the degrees of freedom are n₁ + n₂ − 2.

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