What does the variance of a data set measure?

Variance measures how spread out the values are around the mean. Variance is the mean of the squared deviations from the mean, using n − 1 as the divisor for a sample.

How is standard deviation related to variance?

The standard deviation is the square root of the variance. The standard deviation has the same units as the data, which makes it easier to interpret.

Five repeat readings of a reaction time are 12, 15, 14, 11 and 13 seconds. What is their standard deviation?

The sample standard deviation is 1.58 s. The mean is 13 s, the squared deviations sum to 10, and √(10 ÷ 4) = 1.58 s.

CCEA A-Level Life and Health Sciences 0008

Experimental Techniques

Topic overview Standard solutions, titrations and qualitative tests Rates of reaction and organic preparations Physics measurements: oscillations, resistivity, lenses and critical angle Biological tests, colorimetry, chromatography and osmosis

Human Body Systems

Topic overview Blood vessels, the heart and cardiac output Heart sounds, ECG traces, pulse and blood pressure Body fluids, haemoglobin and the Bohr effect The respiratory system, gas exchange and lung disease Monitoring breathing and lung volumes Cellular respiration and ATP Homeostasis, blood glucose and thyroxine Sodium, blood pH and oxygen saturation A balanced diet and nutritional needs through life Cholesterol, minerals, vitamins, alcohol and exercise

Physical Chemistry in Industrial Processes

Topic overview Moles, reacting masses and percentage yield Titration types, indicators and standard solutions Titration calculations and molarity Enthalpy changes and calorimetry Hess's law and average bond enthalpies Collision theory, rates and the Maxwell–Boltzmann distribution Catalysts, chemisorption and catalytic converters Reversible reactions, the Haber process and the Contact process Scale-up, costs and siting a chemical plant

Brain ScienceDouble Award

Topic overview Brain structure and frontal lobe damage Neurones, synapses and the endocrine system Alzheimer's disease, Huntington's disease and stem cell therapy Schizophrenia and mental health awareness in Northern Ireland The biology of aggression and methods of studying the brain Stress, the stress response and stress management Memory models, forgetting and eyewitness testimony Abnormality, phobias, depression and OCD Experiments, observations, self-report and research design Hypotheses, sampling, ethics and descriptive statistics

Material ScienceDouble Award

Topic overview Material properties and selection Stress, strain and the Young modulus Stress–strain graphs, creep and fatigue Density, hardness and conductivity testing Metals, ceramics, glasses, polymers and composites Atomic and microscopic structure of materials Alloys, annealing and biomaterials Smart materials Nanomaterials and semiconductors

Medicine, Drugs and Clinical TrialsDouble Award

Topic overview Categories of medicine and routes to drug discovery Medicines from natural sources, drug names and the ATC system Drug development, preclinical testing and the therapeutic index Phases of clinical trials and trial design Licensing, UK regulators, Yellow Card and trial ethics Formulations, routes of administration and drug absorption Distribution, metabolism, elimination and sites of drug action Quantitative analysis of medicines and antibacterial bioassays

Scientific Method, Investigation, Analysis and Evaluation

Topic overview The scientific method, literature reviews and Harvard referencing Descriptive statistics and the normal distribution Null hypotheses, significance and choosing a statistical test Investigation design, Design of Experiments and project plans Good Laboratory Practice, risk assessment and COSHH Experimental error, scientific writing and evaluation

Organic Chemistry

Topic overview Organic formulae, homologous series and functional groups IUPAC naming and types of organic reaction Structural isomerism and E/Z isomerism Alkanes from crude oil, combustion and halogenation Vehicle pollutants, catalytic converters and biofuels Alkenes, pi bonds and electrophilic addition Classifying alcohols, making ethanol and its effects as a drug Oxidation of alcohols, IR spectroscopy and mass spectrometry Addition polymers, plastic waste and nylon Preparing and purifying aspirin

Medical PhysicsA2 option

Topic overview Body temperature and clinical thermometers Blood pressure readings and the sphygmomanometer Heart activity experiments and EEG traces X-ray tubes, radiographs and CT scans Flexible endoscopes, optical fibres and lasers Ultrasound A-scans, B-scans and acoustic impedance MRI scanning and gamma camera imaging Alpha, beta and gamma radiation and half-life Radiopharmaceuticals, radiotherapy and radiation protection

Sound and LightA2 option

Topic overview Transverse and longitudinal waves and wave graphs Phase difference and the electromagnetic spectrum Outer, middle and inner ear Sound intensity and the decibel scale Standing waves, harmonics and resonance tubes Hearing response, phons and equal loudness curves Structure of the eye, rods and cones Accommodation, lens power and correcting long sight Total internal reflection and fibre-optic communication Dipole antennas, wireless networks and radar Attenuation of radio waves and the Doppler effect

Genetics, Stem Cell Research and CloningA2 option

Topic overview DNA structure and the evidence for the double helix RNA, genes and the triplet code Genotype, phenotype and monohybrid inheritance Dihybrid crosses, epistasis and the chi-squared test DNA replication and the Meselson–Stahl experiment Meiosis and genetic variation Insulin, factor VIII and chymosin from genetically modified microbes Recombinant DNA technology and gene cloning Genetic engineering, food supply and ethics Gene therapy and cystic fibrosis Genetic disease, screening and counselling Genetic fingerprinting and gel electrophoresis Stem cells, therapeutic cloning and their ethics

MicrobiologyDouble Award

Topic overview Bacteria, fungi and protozoa Viruses, viroids and prions Classifying bacteria, fungi and viruses Light and electron microscopy Laboratory safety, biocontainment and quality assurance Aseptic technique, growth media and inoculation Counting and measuring microbial growth Growth requirements and growth inhibition Antibiotics, PCR, gene therapy and pharmaceutical microbiology The gut microbiome in health and disease

Oral Health and DentistryDouble Award

Topic overview Structure of the mouth and the five basic tastes Salivary glands, saliva and the composition of teeth Ingestion, teeth and digestion in the mouth Dental caries and acid erosion Periodontal disease, tooth loss and dental antibiotics Dental materials, prosthodontics and the dental team

Histology and PathologyDouble Award

Topic overview Specimen processing, data protection and safety law Clinical biochemistry tests and electrophoresis Blood smears and identifying blood cells Blood grouping, cross-matching and transfusion Diagnostic and surveillance work in hospital microbiology Preparing and staining tissue sections Recognising tissues, atheroma and emphysema on slides

Analytical Chemistry TechniquesDouble Award

Topic overview Volumetric analysis in industry and healthcare Applied titrations of vinegar, indigestion tablets and bleach Redox titration of iron tablets and evaluating titrations Principles of colorimetry Colorimetric analysis of copper ore, aspirin and iron Thin-layer chromatography and its uses Visualising chromatograms and identifying painkillers and pigments Calorimetry and combustion Molar enthalpy and bond energy calculations Qualitative tests for cations and gases

Enabling TechnologyDouble Award

Topic overview ECG and EEG machines in patient monitoring Ultrasound and IVF equipment in fertility treatment Prosthetic limbs, hearing aids and cochlear implants Workflow and equipment in a medical laboratory Ongoing monitoring of a long-term condition Health data collection, databases and data protection

Scientific Method, Investigation, Analysis and Evaluation

Descriptive statistics and the normal distribution

3 things to know
A2 1

Overview

Mean, median and mode, variance and standard deviation with worked values, the normal distribution, skew, spreadsheets for statistics and why n − 1 is used.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

How do the mean, median and mode differ?

Key term

The resting pulse rates of six people are 68, 72, 72, 75, 80 and 91 beats per minute. What are the mean, median and mode?

Key term

When is the median a better average than the mean?

Questions from this subtopic

Each one with the model answer underneath.

1
How do the mean, median and mode differ?
Model answer
The mean is the sum of the values divided by the number of values. The median is the middle value of the ordered data, and the mode is the most frequent value.
2
The resting pulse rates of six people are 68, 72, 72, 75, 80 and 91 beats per minute. What are the mean, median and mode?
Model answer
The mean is 76.3, the median is 73.5 and the mode is 72 beats per minute. The working for the mean is 458 ÷ 6 = 76.3, and the median is (72 + 75) ÷ 2 = 73.5.
3
When is the median a better average than the mean?
Model answer
The median is better when the data are skewed or contain an extreme outlier. One very large value pulls the mean upwards but barely moves the median.
4
What does the variance of a data set measure?
Model answer
Variance measures how spread out the values are around the mean. Variance is the mean of the squared deviations from the mean, using n − 1 as the divisor for a sample.
5
How is standard deviation related to variance?
Model answer
The standard deviation is the square root of the variance. The standard deviation has the same units as the data, which makes it easier to interpret.
6
Five repeat readings of a reaction time are 12, 15, 14, 11 and 13 seconds. What is their standard deviation?
Model answer
The sample standard deviation is 1.58 s. The mean is 13 s, the squared deviations sum to 10, and √(10 ÷ 4) = 1.58 s.

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