12 Stats Statistics is a body of methods for making wise decisions in the face of uncertainty. W. Allen Wallis

12 Statistics WHY TAKE STATISTICS? We live a world that is filled with uncertainty and variability. The field of statistics exists because of this. Statistical methods allow us to gain information and control because we can use them to measure variability and find predictable patterns in the presence of uncertainty. Here are some reasons why statistical methods are popular and useful: As individuals to help us make personal decisions about things like What to eat to remain healthy How to enhance our children’s well-being Which treatment to undergo in a medical situation How to invest our time to enhance our enjoyment of life As a society we want to have some control over Reducing rates of cancer, heart attack, diabetes and other diseases Growing better plants (pest resistant, high yield, etc) Determining public education strategies to reduce the incidence of HIV Deciding on road safety measures to reduce to road toll As intelligent and curious beings we want to understand things like Psychic abilities – are they real? Are left-handed people better at mathematics? Does listening to classical music enhance our intelligence? Do male and female brains work differently? As social and curious beings we want to know about other people Who are they planning to vote for at the next election? What TV programmes are they watching? How much alcohol do they drink? How much exercise do they take? This course has been designed for students who wish to keep their career options open by studying mathematics at Level 2, for whom the regular course in mathematics is not appropriate. Successful completion of the course provides eligibility for continuing with a Statistics and Modelling course in year 13. The main focus of the course is statistics. You will use and understand the processes of carrying out an investigation to provide an answer to a real problem, using statistics to organise, process, present and analyse the data. You will learn to communicate the findings and make predictions, using technology as an aid. Other topics include using sequences of numbers to solve problems and an introduction to calculus.

Continuing with Statistics A few of the students (about 2 or 3) who successfully complete the course go on to take the full 24 credit Stats and Modelling course that includes external assessment. About 40% of them continue with an internally assessed course in Stats (see later for details).

Use of technology There is a strong technology component. Technology is used for assessment. Skills are developed with Excel Fathom. Casio Power Graphic fx-9750G PLUS

Content overview Surveys and Questionnaires Display of Data Sampling Probability Bi-variate Data or Time SeriesInvestigation Sequences and Series Calculus Some elements of statistical literacy

NCEA This course is entirely internally assessed and provides access to a maximum of 17 Level 2 credits.

Standards offered Standard Title Type Credits Date Time required US 12332 v3 Demonstrate knowledge of measures and displays used to compare data sets Internal 2 Early term 1 2 period in class AS 2.5 (90288) v2 Select a sample and make inferences from the data 3 Late term 1 1 ½ periods in class US 12333 Demonstrate understanding of and use, questionnaire design Early term 2 AS 2.6 (90289) Simulate probability situations and apply the Normal distribution Late term 2 2 periods in class US 5248 Use Sequences & Series to solve problems. Early term 3 US 7564 (Bivariate data investigation) Plan, carry out and report on a statistical investigation into a given area. Late term 3 3 periods in class US 5244 v4 Demonstrate Calculus skills Early term 4 TOTAL CREDITS 17

Processes In addition students who achieve all students using a high level of communication will be eligible to enter Unit Standard 5243 Apply mathematical processes and skills in problems 7 Credits

Questionnaires Unit Standard 12333: 3 Credits Demonstrate understanding of, and use Questionnaire design demonstrate understanding of questionnaire design, and design and trial a questionnaire for a given purpose.

Compare Data Sets Display of data Measures Comparison Box plot, (composite) bar graphs Measures Mean, median Standard deviation, inter-quartile range Comparison Discuss symmetry unusual values compare box plots

Investigation Using time series or Bi-variate data Writing a question Construction of a scatterplot Describe trend Insert a linear trend line Make a prediction

Scatterplot of Final Mark v Coursework for Psychology 1

Sequences and Series Taught and assessed using Excel

13 internally assessed statistics Achievement Objectives To give access to mathematics for students who wish to keep their career options open by studying mathematics at Level 3 for whom the regular course in mathematics is not appropriate To develop skills and understanding in the application of statistics and modelling. To use technology as an aid to solve problems involving the analyses of data. This course has “approved subject” status.

Assessment for qualifications Standard Title Type Credits Date Time required US 5258 V3 Use expected values to solve problems Internal 2 End term 2 1 period in class US 5259 Use probability distribution models to solve problems 3 Middle Term 3 1 period in class AS 90645 V2 Complete a Statistical investigation involving bi-variate data. Middle term 1 2 periods in computer room 90647 V2 Use a mathematical model involving curve fitting to solve a problem End term 1 90641 V2 Determine the trend for time series data. Early term 2 90642 V2 Calculate confidence intervals for population parameters External NCEA External at end of year

The quiet statisticians have changed our world-not by discovering new facts or technical developments but by changing the ways that we reason, experiments and form our opinions Ian Hacking (Science 1984)