• 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.

• #### 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 how to obtain a systematic sample

4. Calculate proportions from a stratified sample

5. Identify the target population - census or sample

6. Describe the process of a statistical investigation

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

1. Interpret a histogram with a log scale

2. Construct frequency histogram and polygon for grouped data

3. Construct a histogram with a log scale

4. Divide large sets of data into percentiles

5. Divide large sets of data into quartiles

6. Analyse a variety of data displays

7. Identify and analyse misleading graphs

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

9. Construct Frequency Distribution Tables: Grouped Data

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

11. Determine logs from numbers

12. Determine numbers from logs

13. Read percentiles from graphs

14. Divide large sets of data into deciles

15. Read quartiles from graphs

16. Interpret a radar chart

17. Construct a radar chart

18. Read deciles from graphs

• #### Bivariate Data 12 concepts

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

2. Calculate residuals

3. Construct the least-squares line of best fit

4. Find the equation of the least-squares line of best fit

5. Demonstrate understanding of correlation and causation

6. Interpret the slope and intercept of a regression line

7. Find the equation of a line of best fit

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

9. Draw a line of best fit on a scatterplot

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

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. Identify key features in a time series plot

3. Smoothing a time series plot using moving means

4. Smoothing a time series plot using moving medians

5. Describing time series plots by identifying key features

6. Construct time series plots

7. Calculate seasonal indices

8. Interpret seasonal indices

9. Deseasonalise data

10. Reseasonalise data

• #### Summary Statistics 16 concepts

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

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

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

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

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

6. Calculate Interquartile Range

7. Calculate the range of ungrouped data sets

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

11. Estimate the median From a cumulative frequency graph

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

13. Finding the Standard Deviation on a Calculator

14. Finding the Mean on a Calculator

15. Finding the Mode From a Frequency Distribution Table

16. Finding the Mean From a Frequency Distribution Table

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

1. display two sets of data on a radar chart

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

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

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

• #### Normal Distribution 2 concepts

1. Calculate the standardised value, called the z-score, of a normal distribution

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

• #### Sampling and Population 4 concepts

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

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

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

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

### 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

Use anytime