• Mathematics General
• Year 12

# Data and Statistics

approx. 25 hrs

8 topics

75 concepts

Develop strong mathematical skills in Data and Statistics to approach your examinations with confidence.

Available in
NT QLD SA TAS VIC WA

### Overview

The Year 12 Data and Statistics program is aligned to the outcomes from the Statistics and Probability Strand in the Australian curriculum. In Data and Statistics, students study statistical processes and inquiry in society, acquire skills in statistical techniques to display and interpret small and large data sets, and apply reasoning in the evaluation and construction of arguments and the interpretation and use of models based on statistical concepts.

### Topics & Concepts We Cover

This learning program is made up of the following 8 topics, broken down into 75 concepts.

• #### Displaying and Interpreting single data sets 18 concepts

1. Construct frequency histogram and polygon for grouped data

2. Construct Frequency Distribution Tables: Grouped Data

3. Construct a histogram with a log scale

4. Interpret a histogram with a log scale

5. Divide large sets of data into quartiles

6. Divide large sets of data into percentiles

7. Analyse a variety of data displays

8. Identify and analyse misleading graphs

9. Identify and explain which graph types are suitable for the type of data being considered

10. Construct frequency tables for grouped data from cumulative frequency graphs

11. Determine logs from numbers

12. Determine numbers from logs

18. Divide large sets of data into deciles

• #### Bivariate Data 12 concepts

1. Calculate residuals

2. Use a residual plot to determine the appropriateness of using the equation of the least squares line to model the association

3. Find the least-squares line of best fit equation given a value for r (correlation coefficient)

4. Construct the least-squares line of best fit

5. Use a least-squares line of best fit to make predictions of data sets

6. Identify causality

7. Classify the correlation coefficient from a scatterplot or given a value for r

8. Use a line of best fit to make predictions of data sets

9. Find the equation of a line of best fit

10. Draw a line of best fit on a scatterplot

11. Construct scatterplots

12. Interpret scatterplots including direction, form and strength

• #### Modelling Time Series 10 concepts

1. Fit a least-squares line to a time series plot and make predictions

2. Construct time series plots

3. Identify key features in a time series plot

4. Describing time series plots

5. Smoothing a time series plot using moving means

6. Smoothing a time series plot using moving medians

7. Deseasonalise data

8. Reseasonalise data

9. Calculate seasonal indices

10. Interpret seasonal indices

• #### Normal Distribution 2 concepts

1. use calculated z-scores to compare scores from different data sets

2. using the z-score to calculate proportion of scores distributed one, two or three standard deviations away from the mean

• #### Sampling and Population 4 concepts

1. apply counting techniques to list all possible samples of varying sizes from a known small population

2. verify that the mean of the distribution of all possible sample means is equal to the population mean for populations

3. use the capture/recapture technique for estimating the size of populations

4. recognise the effect of sample size in estimating the nature of a population

• #### Summary Statistics 16 concepts

1. Estimate the median of a data set from a cumulative frequency polygon for grouped data

2. Estimate the upper and lower quartiles of a data set from a cumulative frequency polygon for grouped data

3. Determine the five-number summary from a stem-and-leaf plot

4. compare summary statistics, including mean, mode, median, and population standard deviation, for two sets of data

5. Establish a five-number summary for a data set

6. Calculate the range of ungrouped data sets

7. Calculate Interquartile Range

8. Construct a box plot using the five-number summary

9. Identify outliers and describe the impact on the measures of centre and spread

10. Finding the Mode From a Frequency Distribution Table

11. Finding the Mean From a Frequency Distribution Table

12. Estimate the median From a cumulative frequency graph

13. select and use the appropriate statistic (mean, median or mode) to describe features of a data set

14. Compare summary statistics from a variety of contexts including measures of centre and measures of spread

15. Finding the Standard Deviation on a Calculator

16. Finding the Mean on a Calculator

• #### Interpreting multiple sets of data 7 concepts

1. determine the percentages of data between any two quartiles on a box-and-whisker plot

2. display two sets of data on a radar chart

3. prepare an area chart to illustrate and compare different sets of data over time

4. Use two-way tables to calculate probabilities

5. display data in two box-and-whisker plots drawn on the same scale

6. Describe the shape of a distribution including skewness and modes

7. display data in double (back-to-back) stem-and-leaf plots

• #### Data Collection and Sampling 6 concepts

1. Creating and evaluating questions as part of the statistical inquiry

2. Identify and select different sampling techniques - simple random, systematic and stratified

3. Calculate proportions from a stratified sample

4. Calculate how to obtain a systematic sample

5. Describe the process of a statistical investigation

6. Identify the target population - census or sample

### What you'll get

Learning Content

• A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
• All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

• We match you to a private, expert tutor who is right for your needs and goals
• Our tutors are talented, tested, top ATAR achievers and subject experts
• During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Data and Statistics

Reporting

• Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
• You and your parents receive a comprehensive feedback report after every session
• Every session is recorded and available for you to watch at any time, allowing you to review what was covered

### Ready to start this program?

Simply pick a time that works for you

We'll book in your first session and match you to an expert tutor

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

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