• Mathematics Standard
• Year 12

# Data and Statistics

approx. 25 hrs

7 topics

59 concepts

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

Available in
NSW

### Overview

Data and Statistics is a learning program that covers the outcomes from the Statistics and Probability components of Year 12 General Mathematics, as defined in the NSW Senior Mathematics syllabus.  In this program, we help students understand statistical processes and inquiry in society, acquire skills in statistical techniques to display and interpret small and large data sets, and apply reasoning when evaluating and constructing arguments when interpreting models based on statistical concepts.

### Topics & Concepts We Cover

This learning program is made up of the following 7 topics, broken down into 59 concepts.

• #### Data Collection and Sampling 6 concepts

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

2. Calculate proportions from a stratified sample

3. Calculate how to obtain a systematic sample

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

5. Describe the process of a statistical investigation

6. Identify the target population - census or sample

• #### Displaying and Interpreting single data sets 14 concepts

1. Divide large sets of data into percentiles

2. Divide large sets of data into quartiles

3. Analyse a variety of data displays

4. Construct frequency histogram and polygon for grouped data

5. Construct Frequency Distribution Tables: Grouped Data

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

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

8. Identify and analyse misleading graphs

13. Divide large sets of data into deciles

• #### Bivariate Data 10 concepts

1. Construct the least-squares line of best fit

2. Demonstrate understanding of correlation and causation

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

4. Interpret the slope and intercept of a regression line

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

6. Construct scatterplots

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

8. Find the equation of a line of best fit

9. Interpret scatterplots including direction, form and strength

10. Draw a line of best fit on a scatterplot

• #### 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 median of a data set from a cumulative frequency polygon for grouped data

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

5. Calculate the range of ungrouped data sets

6. Calculate Interquartile Range

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

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

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

10. Estimate the median From a cumulative frequency graph

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

12. Finding the Standard Deviation on a Calculator

13. Finding the Mean on a Calculator

14. Finding the Mean From a Frequency Distribution Table

15. Finding the Mode From a Frequency Distribution Table

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

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

1. Prepare an area chart to illustrate and compare different sets of data over time

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

3. Display two sets of data on a radar chart

4. Display data in two box-and-whisker plots drawn on the same scale

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

6. Use two-way tables to calculate probabilities

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. Recognise the effect of sample size in estimating the nature of a population

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

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

4. Use the capture/recapture technique for estimating the size of populations

### 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 be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime