DS1 – Statistics and Society, Data Collection and Sampling bar chart bias box- and - whisker plot categorical data census class interval continuous cumulative frequency histogram polygon data decile discrete divided bar graph dot plot five-number summary frequency table grouped data interquartile range mean measure of location measure of spread median modal class mode nominal ordinal outlying value percentile poll population quantitative data quartile questionnaire radar chart random sample range sample sample size sector graph spread standard deviation statistical display statistical inquiry stem-and-leaf plot stratified sample summary statistics systematic sample ungrouped data upper / lower extreme upper / lower quartile

Basic concepts: Investigate ways of collecting, displaying, summarising and analysing data Identify the target population and decide whether sampling or a census is required Classify data as either quantitative or categorical Distinguish between types of sampling and which is most appropriate for a situation Identify types of bias in data

Types of Questions When we need to find out information, there are different ways to phrase questions:

Types of Variables:

Sample or Census? When collecting data we need to consider the target population (the entire group from whom information is to be collected). There are two ways to collect information – a census or a sample. When would it be more appropriate to use a sample? Give some examples.

Bias The major challenge in collecting information is to make it as ‘bias-free’ as possible. A biased sample is one where the data has been influenced by the collection process and is not truly representative of the whole population. e.g. Tasha wants to know about social media use on the Central Coast, so she asks all the girls in her maths class about their online presence. Where is the bias? How could it be avoided? e.g. Sarah wants to find out about the time the average commuter spends travelling to work, so she goes to the local railway station on a Tuesday morning at 10 a.m. and asks every person there. Where is the bias? How could it be avoided?

Random Sampling Random sampling means that every member of a population has an equal chance of being selected in a sample. Drawing peoples names at random or using a random number generator are some ways of ensuring a random sample.

Stratified Sampling Sometimes we need to have a stratified sample, which means proportional. For example, if you wanted a sample representative of a whole school you may select students from each year; and the number of each would depend on how many students in each year.

Systematic Sampling Another type of random sampling is systematic sampling. Each member of the population is assigned a number, then, for example, every tenth number is included in your sample.

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