The (arithmetic) mean for a set of numerical data is the sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values.

The median is the central (middle) piece of data when the data are in numerical order. It is a measure of central tendency representing the average of the values.

The mode is the most frequent value. It is a measure of central tendency representing the average of the values.

The range is a measure of spread. It is found by finding the difference between the highest and lowest values.

The population is the entire set of people, creatures, plants or items that make up the whole group which is being studied.

Checking understanding of statistical problems

Maths

The Statistical Enquiry Cycle

Types of data

Sampling methods

Stratified sampling

Capture/recapture sampling method

Sampling limitations

Data collection

Biased questioning

Advanced problem solving with sampling

In this unit, pupils are given the opportunity to assess how valid a sample may be and what the averages might tell us. In the future unit, pupils extend their knowledge of averages to stem and leaf diagrams as well as comparing two data sets.

In the prior unit, pupils considered the mean, median and mode and evaluated their usefulness in a variety of contexts. In this unit, pupils are given the opportunity to consider where the data came from and how it was collected and can therefore start to evaluate how good a representation the sample is of the whole population.

In this unit pupils will learn how to sample, and explore accuracy and limitations with various sampling strategies and data collection techniques.

Sampling

The Statistical Enquiry Cycle is a cycle used to carry out a statistical investigation. There are five stages. This is an ongoing process as evaluation may lead to new/refined questioning.

Primary data refers to data that are directly collected for specific use in an investigation. Secondary data refers to data that were previously collected for a different or unknown purpose.

Qualitative data are data that are non-numerical, and usually describe a quality of something.

Quantitative data are numerical data that can be counted or measured.

Discrete data can only take specific numerical values.

Continuous data can take any value on a scale to as much precision as we can measure it.

A simple random sample is where every item in a population has an equal chance of being selected for the sample.

A population may be split intro strata (groups). Each stratum is distinct and each item in the population can only belong to one stratum.

A stratified sample is where a representative sample is taken from each stratum.

Capture-recapture is a sampling method which allows us to estimate the size of a population without counting it fully. It is very useful when the entire population may be too difficult to count.

Bias can be present in any sample collected from a population and may affect the results of a statistical investigation.

A questionnaire is a set of written questions designed to collect information from a respondent.

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