The Statistical Enquiry Cycle Lesson Objective To learn

The Statistical Enquiry Cycle

Lesson Objective To learn the components of the Statistical Enquiry Cycle Lesson Success Criteria • Can describe each component of the Statistical Enquiry Cycle

Overview Statistics is about the collection and summarising of data from the world around us. Why? • Business analysis – profits, market research, product design, pricing, advertising • Sport and recreation – analysis, performance • Health and medicine – understanding, providing answers – cures • Government and council planning Statistics are everywhere we look, and used throughout all professions. Technology has taken over the handling of data, but we still rely on human interpretation of the results, in relation to the relative context to understand what they actually mean.

Population vs Sample Population - refers to all members of a group e. g. all Year 11 students in NZ Sample - refers to a smaller group of the population e. g. Year 11 students in this class We collect data from a sample, as the population is too large to handle, (too costly, takes too long etc). The sample data is analysed and then used to gain an insight about the population. The sample needs to be at least 30, for it to have some accuracy - a sample is a ‘snapshot’ of the population - a different sample will give different results

Problem This is where you decide what you would like more information about. This stage involves defining the problem of interest, and posing a question. Consideration of variables (the characteristics of interest that are being measured) need to be carefully defined and understood. We will be only working with comparison questions within this standard. The question would normally be written “I wonder if …” You should provide some thought or comment, as to what answer you would predict to the question you ask. NOTE: The question needs to written in a very specific way.

Plan You need to know what you will measure and how you will do it. Consider the following thing: Ø What data do you need to collect? Ø How much data is needed? Ø How will you collect the data in order to answer the question? Ø What measurement system will be used for the variables? Ø How will the data be recorded? Ø What problems could arise in the collection of the data? NOTE: for this standard, and assessment, you will be provided the data. However you will be expected to mention where it came from, and discuss any potential problems that could of have arisen in its collection.

Data This is where your data is collected, managed and organised. Raw data is collected according to the plan. Decide on a sampling plan. If using an existing data set, take a sample from it. Decisions then need to be made, on whether the data needs to be cleaned, and sorted prior to being analysed. Often the data is organised in a way that it is easy to extract the information from i. e. a table

Analysis This is where you look at the data to see what it tells you about your problem. i. e. summarising and making sense of the data, so you can answer your question This will involve Ø Display the data into relevant tables and graphs Ø Calculate statistical measures which summarise your data • Central Tendency (averages: mean, median, mode) • Spread (range, interquartile range) Ø Using “I notice…” statements in relation to your observations of any patterns, or special features of the data set • Unusual values (outliers) • Symmetry of distribution Ø Are your predictions still the same, or would you change them? NOTE: it is important that any statements are supported with evidence

Conclusion What did you learn from your investigation? Start by answering your question first posed in the Problem stage - with justification, based on the analysed data Ø Ø Ø What do the graphs tell you? What differences are there in the statistics? Can you infer that any difference in the sample is also in the population? Suggest possible sources of error Suggest improvements Does the investigation suggest new problems that could be investigation? NOTE: always mention any other important aspects of the investigation. Using statistical insight is vital for ongoing statistical studies. Using “what if” statements show your ability to think.

SUMMARY We will be conducting an investigation using the statistical enquiry cycle P - roblem P - lan D - ata A - nalysis C - onclusion You will be making the decision on what variables to investigate, providing an investigative question, gathering the data, analysing it, and providing a sound, justified conclusion to your question.

Reflection What vocabulary have we used today?

Homework Chapter 7 Exercise A: