What is the mean, and how is it found?

The mean is the arithmetic average: all the values in a set are added together and the total is divided by the number of values. It uses every value in the data set, which makes it the most complete summary of a set of measurements, and it is the average that most statistical work is built on.

What is the mode, and what makes it different from the other averages?

The mode is the value or category that occurs most frequently in a data set. It differs from the mean and median in that it is not calculated from the size of the values at all - it is simply a count of frequency - which means it is the only average that can be used with categories that have no numerical value, such as the commonest land use, the commonest rock type or the most frequent answer on a questionnaire. A data set can have two modes, or none at all if every value is different.

What is the range, and what does it tell you?

The range is the difference between the highest and the lowest value in a set, found by subtracting the smallest from the largest. It is a measure of dispersion rather than of average: it tells you how spread out the data are, and therefore how much variation the average is hiding.

When is the median the better average, and why?

When the data are skewed or contain a few extreme values, because the median depends only on the position of values in the ordered list and not on their size, so a single very large or very small figure moves it hardly at all. That is why incomes, house prices and river discharges are usually summarised by the median: it describes the typical case rather than being distorted by the extremes. It is also the better choice for ordinal data, such as scores on a bipolar environmental quality scale, where the intervals between the ranks are not truly equal.

CCEA A-Level Geography 3910

Processes That Shape Fluvial Environments

Topic overview The drainage basin as an open system Storm hydrographs Factors influencing storm hydrographs Annual hydrographs and river regimes River erosion and transportation Deposition and the Hjulstrom curve Erosional and mixed river landforms Depositional river landforms

Human Interaction in Fluvial Environments

Topic overview Why rivers are channelised, and the methods used Environmentally sensitive and sustainable river management The causes of river flooding The effects of flooding on people, property and land

Global Biomes

Topic overview The global distribution of biomes The tundra biome: climate and soils The temperate grassland biome: climate and soils Climate change and tundra ecosystems

Small-Scale Ecosystems

Topic overview Biotic and abiotic components Ecosystems as open systems Trophic structure and ecological pyramids Nutrient cycling and the nutrient cycling model Plant succession and seral stages Climatic climax and plagioclimax vegetation

The Processes That Shape Our Weather and Climate

Topic overview The global energy balance Vertical and horizontal heat transfer in the atmosphere Ocean currents and the transfer of heat Pressure belts, the Coriolis effect and the pressure gradient The tri-cellular model, the global winds, and where it breaks down Jet streams and the upper westerly winds Global patterns of temperature, pressure, wind and precipitation Factors influencing air temperature

Weather in the British Isles

Topic overview How precipitation forms Air masses affecting the British Isles The polar front and the birth of a depression The life cycle of a depression, and its fronts The sequence of weather as a depression passes Anticyclones in summer and winter Isobars, wind, and the front symbols on a synoptic chart Station circles, recognising systems, and satellite images

Global Weather Issues

Topic overview The Pacific in a normal year: the Walker circulation El Niño events and their global consequences La Niña events and their global consequences How tropical cyclones form The structure of a tropical cyclone The impacts of a tropical cyclone on people and property Managing tropical cyclones: prediction, preparation and response

Population Data

Topic overview Census taking, vital registration, and how the data is collected The reliability of the data, and the use made of it

Population Change

Topic overview Fertility and mortality measures, and why crude rates are crude The demographic transition model The epidemiological transition

Population and Resources

Topic overview Overpopulation, underpopulation and optimum population Malthus and Boserup, and how they hold up Fertility policies, and evaluating one

Settlement Change and the Rural-Urban Fringe

Topic overview Defining rural and urban settlement The rural-urban continuum Issues affecting the rural-urban fringe Greenfield and brownfield development Suburbanisation Counterurbanisation

Planning in Rural Environments

Topic overview Why the countryside needs planning protection ASSIs and SSSIs Areas of Outstanding Natural Beauty National parks A national park for Northern Ireland: the case for, the case against, and the verdict

Urban Challenges in MEDC and LEDC Cities

Topic overview Economic and social deprivation in the MEDC inner city Re-urbanisation in the MEDC city Gentrification and its consequences Urban growth and informal settlements in the LEDC city Service provision in the LEDC city Economic activity and the informal economy in the LEDC city

Measuring Development

Topic overview Why 'development' resists definition Two economic measures: GDP and GNI per capita Two social measures: infant mortality and adult literacy Two composite measures: the HDI and the Gender Inequality Index Using the measures together to describe global contrasts

Reducing the Development Gap

Topic overview The Millennium Development Goals: aims and framework Evaluating two Millennium Development Goals The 2030 Agenda and the Global Goals How the Global Goals build on the Millennium Development Goals Globalisation as a route to development in LEDCs Aid and development in LEDCs, and judging development in one

Emerging Markets

Topic overview What an emerging market is BRICS and MINT: what the labels group, and why they are contested Why emerging markets have grown, and one economy studied

Data Collection

Topic overview Collecting primary data in the field Sampling methods: random, systematic, stratified and pragmatic Point, line and quadrat sampling Ordnance Survey maps and map reading Photographs and satellite images as evidence Synoptic charts and remotely sensed data

Data Processing

Topic overview Geographical information systems, and mapping techniques Annotated sketch maps, and the graph types Triangular graphs Mean, median, mode and range Spearman's rank correlation Nearest neighbour analysis Chi-squared (A2 only)Location quotient (A2 only)Developing investigative skills, and the conventions of mapping and graphical work

Fieldwork Skills and Techniques

Topic overview Framing a geographical question and designing the enquiry Fieldwork safety, hazards and contingency planning Choosing and justifying sampling techniques for an investigation Collecting quantitative and qualitative evidence Describing and evaluating data collection methods Presenting evidence in cartographic, diagrammatic and graphical form Choosing and applying statistical techniques Analysing evidence and drawing conclusions Evaluating methods, evidence and the limitations of conclusions

Planning and Recording an Investigation

Topic overview Choosing an issue, hypothesis or question Identifying appropriate sources and methods Describing the study area, stating aims, and recording data

Plate Tectonics: Theory, Margins and LandformsTectonics

Topic overview The structure of the Earth and the driving mechanism The evidence for continental drift and plate tectonics Constructive margins: processes, ocean ridges and rift valleys Conservative margins: processes and why they build nothing Destructive margins: subduction, trenches and island arcs Collision margins and fold mountains Matching landform to margin: the classic confusions

Volcanic Activity and Its ManagementTectonics

Topic overview Magma composition, viscosity and eruption style Volcanic activity at constructive margins Volcanic activity at destructive margins Hot spots and intraplate volcanic activity Hazards of volcanic activity Benefits of volcanic activity Preparing for volcanic activity: monitoring, planning and protection Responding to volcanic activity and evaluating the response

Seismic Activity and Its ManagementTectonics

Topic overview The nature of a seismic event Seismic waves: P, S and L waves Seismic shaking and its impacts Liquefaction Tsunamis Attempts to predict seismic events Preparing for seismic activity Responding to seismic activity and evaluating the response

Locations and Climates of the Major Tropical BiomesTropical

Topic overview The Hadley cell and the ITCZ Tropical forest: distribution, climate and biomass Tropical grassland: distribution, climate and biomass Hot desert, and the tropical biomes compared

Management and Sustainability in Arid and Semi-Arid Tropical EcosystemsTropical

Topic overview Why irrigation is needed, and the methods used The benefits of irrigation and its environmental problems The socio-economic problems of irrigation, and the solutions

Management and Sustainability in the Tropical Forest EnvironmentTropical

Topic overview Trophic structure, the nutrient cycle, and why clearance is so damaging The zonal soil of the tropical forest Large-scale development and its threats to the forest ecosystem Attempts to achieve sustainable development in the tropical forest

Coastal Processes and FeaturesCoastal

Topic overview Waves and wave energy Wave refraction and coastal alignment Marine erosion, transport, longshore drift and deposition Landforms of high-energy coasts Landforms of low-energy coasts

Regional Coastlines: Submergence, Emergence and Rising Sea LevelCoastal

Topic overview Eustatic and isostatic change Coastlines of submergence Coastlines of emergence Rising sea level and the threat of climate change

Coastal Management and SustainabilityCoastal

Topic overview Environmental Impact Assessment and Cost-Benefit Analysis Sediment cells and Shoreline Management Plans Hard engineering strategies Soft engineering strategies Choosing and evaluating a management strategy

Natural Climate Change: Evidence, Causes and the Arrival of the HoloceneClimate

Topic overview Evidence for past climate change: ice cores, pollen and ocean-floor deposits Causes of long- and medium-term climate change The end of the last glaciation and the arrival of the Holocene

Lowland Glacial LandscapesClimate

Topic overview Ice sheet formation and glacial and fluvioglacial processes Landforms of glacial deposition: till, drumlins, moraines and erratics Landforms of fluvioglacial deposition: eskers and outwash plains Socio-economic development in lowland post-glacial environments

Current Global Climate Change: Human Causes and ImpactsClimate

Topic overview The greenhouse effect and the enhanced greenhouse effect Evidence for recent climate change and its links to human activity Present and potential impacts of climate change

Managing Global Climate ChangeClimate

Topic overview Mitigation: reducing greenhouse gas emissions and capturing carbon Adaptation: reducing vulnerability to climate change International action: the Kyoto Protocol, the IPCC and progress so far

Cultural Groups, Social Inequality and LandscapeCultural

Topic overview Why cultural groups exist Differences between cultural groups Cultural nationalism and its expression Social inequality: exclusion and discrimination as distinct mechanisms Inequality by ethnicity, race, religion, gender, sexuality and class Social constructions of nature and landscape

MigrationCultural

Topic overview Push and pull factors: economic, social, political, cultural and environmental Barriers to migration, and its implications for services, the economy and stability Voluntary and forced migration, and immigration as a political issue

The Geographies of CyberspaceCultural

Topic overview Cyberspace, economic change and cultural globalisation Minority cultures, virtual communities and the digital divide

Sustainable Development in SettlementsPlanning

Topic overview Sustainability, and the urban ecological footprint Carbon footprints and waste management Energy consumption and water supply

Urban Design, Planning and Management for SustainabilityPlanning

Topic overview Eco-towns, eco-cities, residential space and defensible space How greenfield and brownfield development relate to sustainability Retail parks, leisure facilities and open space

Traffic and TransportPlanning

Topic overview The sustainability of transport by sea, air and land Public transport, integrated networks, and restrictions on car use Pedestrian and cycling policies, and judging a traffic management strategy

Defining EthnicityEthnic

Topic overview Race, nationality, language and religion as defining factors Ethnicity as socially constructed and self-ascribed Role, residential concentration, age and gender in perceived identity

Processes That Create and Maintain Ethnic DiversityEthnic

Topic overview Colonisation, annexation and international migration Segregation as a process maintaining diversity Multiculturalism as a process maintaining diversity Economic, social and spatial outcomes of ethnic diversity

Ethnic ConflictEthnic

Topic overview The causes of ethnic conflict The nature of ethnic conflict Social, economic and territorial outcomes of ethnic conflict Ethnic cleansing, international intervention and peace processes

The Changing Nature of TourismTourism

Topic overview The growth of mass tourism as a global industry Positive social and economic impacts of tourism The pleasure periphery and the Butler model of resort development

Challenges and Management of Mass TourismTourism

Topic overview The challenges arising from mass tourism Strategies to reduce the negative impacts of mass tourism

Ecotourism: Opportunities, Challenges and RegulationTourism

Topic overview Defining ecotourism The benefits of ecotourism The negative impacts of ecotourism Regulating ecotourism internationally

Decision Making in Geography

Topic overview What a decision-making exercise asks of you Adopting and maintaining a role Reading maps as evidence Reading photographs as evidence Reading statistics and data as evidence Reading reports and written sources as evidence Reading infographics and diagrams as evidence Processing and presenting supplied quantitative data Interpreting and evaluating the information provided Examining conflicting values Considering alternative choices Making and justifying a recommendation on greater overall benefits Structuring and supporting the decision

Data Processing

Mean, median, mode and range

3 things to know
Unit AS 3

Overview

How each average is found and what the range adds, when the mean misleads, and when the median or the mode is the only one worth using.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

What is the median, and how do you find it when there is an even number of values?

Key term

When is the mean misleading?

Key term

When is the mode the only average you can use?

Questions from this subtopic

Each one with the model answer underneath.

1
What is the mean, and how is it found?
Model answer
The mean is the arithmetic average: all the values in a set are added together and the total is divided by the number of values. It uses every value in the data set, which makes it the most complete summary of a set of measurements, and it is the average that most statistical work is built on.
2
What is the median, and how do you find it when there is an even number of values?
Model answer
The median is the middle value once the data are arranged in order of size, so that half the values lie above it and half below. With an odd number of values it is simply the middle one. With an even number there is no single middle value, so the two central values are added together and divided by two, and that figure is the median.
3
What is the mode, and what makes it different from the other averages?
Model answer
The mode is the value or category that occurs most frequently in a data set. It differs from the mean and median in that it is not calculated from the size of the values at all - it is simply a count of frequency - which means it is the only average that can be used with categories that have no numerical value, such as the commonest land use, the commonest rock type or the most frequent answer on a questionnaire. A data set can have two modes, or none at all if every value is different.
4
What is the range, and what does it tell you?
Model answer
The range is the difference between the highest and the lowest value in a set, found by subtracting the smallest from the largest. It is a measure of dispersion rather than of average: it tells you how spread out the data are, and therefore how much variation the average is hiding.
5
When is the mean misleading?
Model answer
Whenever the distribution is skewed or contains extreme values, because the mean uses every value and so is dragged towards the outliers. One flood peak in a set of discharge readings, or one multi-million pound property among ordinary houses, pulls the mean upwards so far that it no longer describes a typical case, and it can end up being a value that no individual case comes close to. It is also misleading with a bimodal distribution, where two clusters produce a mean sitting in the empty ground between them, and with categorical data, where an average is meaningless.
6
When is the median the better average, and why?
Model answer
When the data are skewed or contain a few extreme values, because the median depends only on the position of values in the ordered list and not on their size, so a single very large or very small figure moves it hardly at all. That is why incomes, house prices and river discharges are usually summarised by the median: it describes the typical case rather than being distorted by the extremes. It is also the better choice for ordinal data, such as scores on a bipolar environmental quality scale, where the intervals between the ranks are not truly equal.

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Global Biomes

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