A-Level Maths Collecting Data
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- Created by: Jamie Hall
- Created on: 20-01-21 15:18
Simple random sampling
In this sampling method, the items in the sample are chosen by a random procedure
such as drawing tickets out of a box or using a random number generator. Every
possible sample of the required size has the same probability of being selected.
such as drawing tickets out of a box or using a random number generator. Every
possible sample of the required size has the same probability of being selected.
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Cluster sampling
If the population is divided into subgroups which are each reasonably representative
of the entire population, then cluster sampling means taking a sample from just a few
of these subgroups.
of the entire population, then cluster sampling means taking a sample from just a few
of these subgroups.
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Opportunity sampling
In opportunity sampling, individuals are chosen to be part of a sample as opportunity
arises. Interviewing passers by on the street is one example.
arises. Interviewing passers by on the street is one example.
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Stratified sampling
If the parent population can be divided into subgroups, or strata, such as by age or
gender, then stratified sampling ensures that all strata are sampled.
gender, then stratified sampling ensures that all strata are sampled.
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Quota sampling
A quota sample is similar to a stratified sample but it is specified in terms of the number of data items required in each stratum.
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Self-selected sample
In a self-selected sample, the individuals in the sample have chosen to be in the
sample. For example, the respondents to a survey posted publicly on the internet are
a self-selected sample.
sample. For example, the respondents to a survey posted publicly on the internet are
a self-selected sample.
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Systematic sampling
A method of choosing individuals to form a sample. For example, if the
parent population was all the Year 11 students in a school, you might obtain an
alphabetical list of the students and select every 10th student on the list.
parent population was all the Year 11 students in a school, you might obtain an
alphabetical list of the students and select every 10th student on the list.
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Statistical Hypothesis
A statement that can be tested by collecting, presenting and analysing data.
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Primary Data
Data you collect yourself from surveys / experiments / questionnaires.
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Secondary Data
Data you use that has been collected by someone else e.g. information in books / internet
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Qualitative variables
• Variables that take non-numerical values – e.g. colours of cars.
• Data using words e.g. the type of answer to the following question: ‘What is your favourite colour?’
• Data using words e.g. the type of answer to the following question: ‘What is your favourite colour?’
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Quantitative variables
• Variables that take numerical values – e.g. temperature.
• Data using numbers e.g. the type of answer to the following question: ‘How many times did you go to the cinema last month?’
• Data using numbers e.g. the type of answer to the following question: ‘How many times did you go to the cinema last month?’
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Discrete variables
Discrete variables take certain values within a particular range – e.g. shoe size.
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Continuous variables
Continuous variables can take any value within a particular range – e.g. length
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Categorical data
Data need not be expressed in numbers. They are usually given as categories such as heads or tails, pain level, gender or eye colour.
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Numerical data
Data are expressed as numbers and the values of these numbers have a numerical meaning.
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Population
The entire group of people / things you want to conduct your investigation on is called the population.
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Census
Involves asking every member of the entire population or collecting data in regard to every member of the entire population. It is therefore representative, unbiased and accurate.
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What is capture-recapture?
It is a statistical technique, using samples, to estimate the size of a population.
The proportion of marked individuals in the entire population = The proportion of marked individuals in the sample
The proportion of marked individuals in the entire population = The proportion of marked individuals in the sample
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What assumptions do we have to make when using capture-recapture?
• The population does not change between capture and recapture (no individuals have joined or left)
• The sample taken on both capture and recapture is random (i.e. both samples are representative of the population)
• The markings have not been removed
•
• The sample taken on both capture and recapture is random (i.e. both samples are representative of the population)
• The markings have not been removed
•
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Equation for Frequency (Histogram)
Frequency = Frequency Density x Class Width
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Measures of Central Tendency - Mean
The mean includes all the data in the average and takes account of the numerical value of all the data. So exceptionally large or small items of data can have a large effect on the mean – it is susceptible to outliers.
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Measures of Central Tendency - Median
The median is less sensitive to high and low values (outliers), as it is simply the middle value in order of size. If the numerical values of each of the items of data is relevant to the average, then the mean is a better measure; if not, use the median.
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Outliers
An outlier is an extreme value in a set of data.
An outlier can be identified as follows:
• Any data which are 1.5 x IQR below the lower quartile;
• Any data which are 1.5 x IQR above the upper quartile.
An outlier can be identified as follows:
• Any data which are 1.5 x IQR below the lower quartile;
• Any data which are 1.5 x IQR above the upper quartile.
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Bivariate Data
Data with two variables
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Regression
Is the act of setting the parameters of our model (here the gradient and y-intercept of the line of best fit) to explain the data.
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Interpolating
Estimating a value inside the data range
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Extrapolating
Estimating a value outside the data range
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Independent Event
Events where the outcome of one does not affect the other.
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Mutually Exclusive
If two events are mutually exclusive they can’t happen at the same time
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Other cards in this set
Card 2
Front
Cluster sampling
Back
If the population is divided into subgroups which are each reasonably representative
of the entire population, then cluster sampling means taking a sample from just a few
of these subgroups.
of the entire population, then cluster sampling means taking a sample from just a few
of these subgroups.
Card 3
Front
Opportunity sampling
Back
Card 4
Front
Stratified sampling
Back
Card 5
Front
Quota sampling
Back
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