GCSE Statistics (Edexcel) (final ver.)

What is raw data?

Unprocessed data that has just been collected and needs to be ordered, grouped, rounded, cleaned.

What is qualitative data?

Non-numerical, descriptive data such as eye/hair colour or gender. Often subjective so usually more difficult to analyse.

What is quantitative data?

Numerical data that can be measured with numbers. Easier to analyse than qualitative data. Example, height, weights, marks in an exam etc.

What is discrete data?

Data that only takes particular values (not necessarily whole numbers) such as shoe size or number of people.

What is continuous data?

Data that can take any value e.g. height, weight.

What is categorical data?

Data that can be sorted into non-overlapping categories such as gender. Used for qualitative data so that it can be more easily processed.

What is ordinal data?

Quantitative data that can be given an order or ranked on a rating scale, e.g. marks in an exam.

What is bivariate data?

Data that involves measuring 2 variables. Can be qualitative or quantitative, grouped or ungrouped. Usually used with scatter diagrams where the two axes represent the two different variables.

What is multivariate data?

Data that is made up of more than 2 variables e.g. comparing height, weight, age and shoe size together.

What does grouping data mean?

Grouping data using tables makes it easier to spot patterns in the data and quickly see how the data is distributed.

What are the pros of grouping data?

Makes the data easy to read and understand, easy to spot patterns and compare data.

What are the cons of grouping data?

Loses accuracy of data as you no longer know exact data values. Calculations made from these will only be an estimate e.g. mean.

What is primary data?

Data that you have collected yourself, or someone has collected on your behalf.

What is secondary data?

Data that has already been collected.

What is a population in the context of an investigation?

Everyone or everything that could be involved in the investigation.

What is a census?

A survey of the entire population.

What is a sample?

A smaller number from the population that you actually survey. The data obtained from the sample is then used to make conclusions about the whole population.

What is a sampling frame?

A list of all the members of the population. This is where you will choose the sample from.

What is a sampling unit?

The people that are to be sampled e.g. students in a school.

What is a biased sample?

A sample that does not represent the population fairly. Example, if surveying students at a mixed school and the sample only contains girls.

What is a random sample?

A sample where every item/person in the population has an equal chance of being selected.

What are some random sampling techniques?

Pick numbers/names out of a hat, using a random number table, using the random number generator function on a calculator or computer.

What are the advantages of random sampling?

Sample is representative as every member of the population has an equal chance of being selected. It's unbiased.

What are the disadvantages of random sampling?

Need a full list of population (not always easily obtainable), not always convenient as it can be expensive and time consuming, needs a large sample size.

What is a stratified sample?

A sample where the size of each strata (group) in the sample is in proportion to the sizes of strata in the population.

What is the method for stratified sampling?

Split the population into groups, use the formula 𝒔𝒕𝒓𝒂𝒕𝒊𝒇𝒊𝒆𝒅 𝒔𝒂𝒎𝒑𝒍𝒆 = 𝒔𝒕𝒓𝒂𝒕𝒂/𝒕𝒐𝒕𝒂𝒍 × 𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒊𝒛𝒆 to calculate sample size for each group, and use random sampling to select members from each strata/group.

What are the advantages of stratified sampling?

Sample is in proportion to population, so sample represents the population fairly. Best used for populations with groups of unequal sizes.

What are the disadvantages of stratified sampling?

Time consuming.

What is systematic sampling?

A method of choosing items in the population at regular intervals.

What is the method for systematic sampling?

Divide your population size by sample size to calculate the intervals, use random sampling to generate a number between 1 and the answer to your calculation from above to choose a starting point, select every nth item after the starting point until you obtain your sample size.

What are the advantages of systematic sampling?

Population is evenly sampled, can be carried out by a machine, sample is easy to select.

What are the disadvantages of systematic sampling?

Not strictly a random sample as some member of the population cannot be chosen.

What is cluster sampling?

A method where the population is divided into natural groups (clusters), groups are chosen at random and every member of groups are sampled.

What are the advantages of cluster sampling?

Economically efficient - less resources required. Can be representative if lots of small clusters are sampled.

What are the disadvantages of cluster sampling?

Clusters may not be representative of the population and may lead to a biased sample. High sampling error.

What is quota sampling?

A method where population is grouped by characteristics and a fixed amount is sampled from every group.

What is the method for quota sampling?

Group population by characteristics e.g. gender and age, select quota (amount) for each group e.g. 30 men under 25, 40 women over 30 etc., obtain sample by finding members of each group until quota is reached.

What are the advantages of quota sampling?

Quick to use, cheap, do not need sample frame or full list of the population.

What are the disadvantages of quota sampling?

Not random - biased as interviewer is choosing who will be in the sample so every member of the population does not have an equal chance of being selected.

What is opportunity sampling?

Using the people/items that are available at the time.

What are the advantages of opportunity sampling?

Quick, cheap, easy.

What are the disadvantages of opportunity sampling?

Not random. The sample has not been collected fairly so it may not represent the population and every member of the population has not been given an equal chance to be selected.

What is judgement sampling?

When the researcher uses their own judgement to select a sample, they think will represent the population.

What are the advantages of judgement sampling?

Easy, quick.

What are the disadvantages of judgement sampling?

Not random. Quality of sample depends on the person selecting the sample. The researcher may be biased and unreliable in the sample they select.

What is Petersen Capture-Recapture?

A method used to estimate the size of large or moving populations where it would be impossible to count the entire population.

What are the assumptions of Petersen Capture-Recapture?

Population has not changed - no births/deaths, probability of being caught is equally likely for all individuals, marks/tags not lost, sample size is large enough and is representative of the population.

What are experiments used for in research?

Used when a researcher is interested in how changes in one variable affect another.

What are the types of variables in experiments?

Explanatory (Independent) Variable - The variable that is changed. Response (dependent) variable - The variable that is measured. Extraneous Variables - Variables you are not interested in but that could affect the result of your experiment.

What is a laboratory experiment?

A type of research where the researcher has full control over variables and it's conducted in a lab or similar environment.

What are the advantages of laboratory experiments?

Easy to replicate, making results more reliable. Extraneous variables can be controlled so results are more likely to be valid.

What are the disadvantages of laboratory experiments?

People may behave differently under test conditions than they would under real-life conditions, which could affect the validity of results.

What is a field experiment?

An experiment carried out in the everyday environment where the researcher has some control over the variables.

What are the advantages of field experiments?

More accurate as they reflect real-life behavior.

What are the disadvantages of field experiments?

Cannot control extraneous variables, not as easy to replicate, making them less reliable than lab experiments.

What is a natural experiment?

An experiment carried out in the everyday environment where the researcher has no or very little control over the variables.

What are the advantages of natural experiments?

They reflect real-life behavior.

What are the disadvantages of natural experiments?

Low validity due to uncontrolled extraneous variables, difficult to replicate, and cannot control extraneous variables.

What is a simulation in the context of experiments?

A way to model random events using random numbers and previously collected data. These could be used to help you predict what could actually happen in real life.

What are the steps in conducting a simulation?

Choose a suitable method for getting random numbers, assign numbers to the data, generate the random numbers, match the random numbers to your outcome.

What is a questionnaire?

A set of questions used to obtain data from the population/sample. Can be carried out via post, email, phone or face to face.

What are open questions in a questionnaire?

Questions that allow any answer. However, the wide range of different answers makes it difficult to analyse the data.

What are closed questions in a questionnaire?

Questions that have a fixed number of non-overlapping option boxes that only allow for specific answers or opinion scales. This makes data easier to analyse.

What are the features of a good questionnaire?

Easy to understand, uses simple language, avoids leading questions, questions are relevant to the investigation, includes a time frame/unit in the question, includes non-overlapping, exhaustive option boxes, questions should not be offensive/personal/embarrassing, questions which are easy to analyse the results.

What are the problems with questionnaires?

Non-response when people in the sample do not respond to the questionnaire, and sensitive questions that may make people uncomfortable so they may not answer truthfully.

What is the random response method in questionnaires?

A method that uses a random event to decide how to answer a question which ensures that people who answer the question remain anonymous.

What are the steps in conducting a random response method?

Find total who answered questions, find probability (heads) if it is a coin, estimate number of heads - Probability x total, estimate number of "yes" answers that were truthful; Yes answer - estimated number of heads, estimate proportion of people who did the crime = D/C.

What is a pilot study?

A small scale replica of the study to be carried out, used to test the design and methods of the questionnaire.

What are the advantages of a pilot study?

Helps you spot any questions that are unclear or ambiguous, gives you an idea of the response rate, allows you to check the time and costs of the study, checks that closed questions include all the possible answers, can be used to check that the questionnaire collects all the information needed.

What are interviews in research?

A method where you question each person individually. Involves lots of specific questions or a list of topics and can be carried out face to face or over the phone or internet.

What are outliers in collected data?

Values that do not fit in with the pattern or trend of the data. Can be extreme values or incorrectly recorded.

What is cleaning data?

A process of fixing problems with the data. This could be done by identifying and correcting/removing incorrect data values or outliers, removing units or symbols from the data, putting all the data in the same format, deciding what to do about missing data.

What are control groups in experiments?

The control group (sometimes called a comparison group) is used in an experiment as a way to ensure that your experiment actually works. It's a way to make sure that the treatment you are giving is causing the experimental results, and not something outside the experiment.

What is the method for using control groups in experiments?

Use random selection to select 2 groups of people, control and experimental groups. Give the test group the treatment, control group no treatment. Compare results from 2 groups to see how effective treatment is. Conditions must be exactly the same for both groups, only treatment must be different.

What are matched pairs in research?

Two groups of equally matched (age/gender etc.) people used to test the effect of a particular factor. Everything in common except the factor being studied.

What is the purpose of matched samples?

To get better statistics by controlling for the effects of other "unwanted" variables.

What is a hypothesis in research?

A statement (not a question) that can be tested by collecting and analysing data.

What are the stages of an investigation?

Planning, collecting data, processing and representing data, interpreting results, evaluating methods.

What is involved in the planning stage of an investigation?

Choosing the hypothesis, deciding what data to collect (variables), and determining how you will record data (data collection tables).

What is involved in the data collection stage of an investigation?

Choosing data sources (primary/secondary), collection methods (questionnaire/interviews), control factors.

What is involved in the processing and representing data stage of an investigation?

Choosing diagrams and calculations.

What is involved in the interpreting results stage of an investigation?

Drawing conclusions from the results of the diagrams and conclusions.

What is involved in the evaluating methods stage of an investigation?

Looking at the strengths and weaknesses of your data collection methods, planning and diagrams, and how well they helped to test the hypothesis.

What is a database in the context of data representation?

A database is a table with a collection of data. It is a form of secondary data if the data is available online and, in most cases, easily accessible.

What do tables in databases usually contain?

These tables usually contain information from real-life statistics.

What skills are needed to interpret information from tables in databases?

You need to be able to use these tables to identify values, calculate totals/differences/percentages, describe trends and explain inconsistencies.

Why might the percentages in a table not add up to 100%?

One of the main inconsistencies will be that the percentages do not add up to 100% and this is due to rounding errors because individual percentages for columns/rows in the tables have been rounded.

What is a two-way table?

A two-way table has information in two categories and has two variables so the data is called bivariate data.

How do you find missing values in a two-way table?

To find missing values, start with the row or column that has only one value missing. Make sure the grand totals for the rows and columns add up to the same number.

What should you write about when comparing data from two-way tables?

When comparing data from two-way tables, write about comparisons between rows/columns but also individual cells.

What is a pictogram?

A pictogram uses pictures or symbols to represent a particular amount of data. It always has a key to show the amount each symbol represents.

What are some guidelines for drawing a pictogram?

When drawing a pictogram, make sure that each symbol is the same size, the symbols represent numbers that can be easily divided to show different frequencies, spacings are the same in each row, and there is a key to show the frequency that each symbol represents.

What are the characteristics of a simple bar chart?

A simple bar chart has bars of equal width, equal gaps between bars, and frequency on the y-axis.

What is a vertical line graph?

A vertical line graph is similar to a simple bar chart but with lines instead of bars.

What is a multiple bar chart?

A multiple bar chart can be used to compare two or more sets of data. It has more than one bar for each class represented by different colours which is shown in the key.

What is a composite bar chart?

A composite bar chart has single bars split into different sections for each different category. It's usually used to compare different times/days/years.

How do you calculate the frequency of each component in a composite bar chart?

The frequency of each component should be calculated by subtracting the upper frequency of that component with the lower frequency.

What is a stem and leaf diagram?

A stem and leaf diagram is a good way of organising data without losing any of the detail. All the original data is in the diagram but looks simple. It also shows the shape of the distribution.

How do you draw a stem and leaf diagram?

To draw a stem and leaf diagram, put the first digits of each piece of data in numerical order down the left hand side, go through each piece of data in turn and put the remaining digits in the correct row, re-draw the diagram, putting the pieces of data in numerical order, and add a key.

What are back-to-back stem and leaf diagrams?

Back-to-back stem and leaf diagrams show two sets of data sharing the same stem so that you can easily compare them. Numbers closest to the stem are smallest. Use two different keys for each set of data.