• Mathematics General
• Year 12

# Data Analysis

approx. 7 hrs

23 topics

51 concepts

Enrol in Data Analysis to master statistical techniques and analysis.

Available in
VIC

### Overview

In Data Analysis, students will investigate the associations between variables through data displays including plots, histograms and the use of log base 10 scale. Students will gain conceptual understanding of the normal distribution, solving problems applying the empirical rule. We will help students gain proficiency with bivariate data analysis through investigation of practical problems. Students will learn to effectively use the Pearson correlation coefficient to analyse association and causation between two variables. Data transformations of non-linear relationships using square, log or reciprocal transformations will also be explored.

### Topics & Concepts We Cover

This learning program is made up of the following 23 topics, broken down into 51 concepts.

• #### Types of data 2 concepts

1. Recognise variables as categorical or numerical (discrete or continuous)

2. Classification of categorical data as either nominal or ordinal

• #### Dot Plots and Stem-and-Leaf Plots 5 concepts

1. Construct dot plots

2. Interpret dot plots

3. Construct stem-and-leaf plots

4. Interpret stem-and-leaf plots

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

• #### Frequency tables 4 concepts

1. Construct a frequency table including percentage frequencies

2. Constructing a bar and percentage bar chart from a frequency table

3. Interpreting and describing frequency tables and bar charts

4. Construct a frequency for grouped data including percentage frequencies

• #### Frequency histograms 2 concepts

1. Construct a frequency histogram using a CAS calculator

2. Construct a frequency histogram

• #### Base 10 logarithms 3 concepts

1. Evaluate a logarithm giving a positive or negative value

2. Use a CAS calculator to evaluate a number if a log is known

3. Use a CAS calculator to find logs

• #### Using log scales 1 concept

1. Construct a histogram with a log scale

• #### Comparing data distributions 2 concepts

1. Compare location and spread of data distributions

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

• #### Significant figures 1 concept

1. Rounding of whole numbers and decimals to significant figures

• #### Measures of centre 3 concepts

1. Finding the Median From a Frequency Distribution Table

2. Finding the Mean From a Frequency Distribution Table

3. Finding the Mode From a Frequency Distribution Table

• #### Measures of spread 3 concepts

1. Calculate standard deviation step-by-step using the formula

2. Calculate the range of ungrouped data sets

3. Calculate Interquartile Range

• #### Summary statistics and technology 1 concept

1. Use the CAS calculator to calculate summary statistics

• #### Outliers and boxplots 2 concepts

1. Construct a box plot include fencing by identifying outliers

2. Use the criteria to define an outlier to solve problems

• #### Standardised value 2 concepts

1. Calculate the z-score from a normal distribution and interpret the results in terms of the standard deviation

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

• #### Empirical rule 2 concepts

1. Apply the empirical rule and z-scores

2. Use the 68-95-99.7% rule for data one, two and three standard deviations from the mean in practical situations

• #### Statistical investigaion 1 concept

1. Implement the statistical investigation process to answer questions

• #### EV and RV 1 concept

1. Identify independent and dependent variables in bivariate data analysis

• #### Association and two categorical variables 1 concept

1. Identify and describe associations between two categorical variables from a two-way table

• #### Association and categorical and numerical variables 2 concepts

1. Use box plots, dot plots and stem plots to identify and describe associations between a numerical and a categorical variable

2. Construct a scatterplot using technology

• #### Association and two numerical variables 2 concepts

1. Construct a scatterplot using technology

2. Interpret scatterplots including direction, form and strength

• #### Correlation 4 concepts

1. Calculate the coefficient of determination and interpret its value

2. Calculate Pearson's correlation coefficient using technology

3. Demonstrate understanding of correlation and causation

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

• #### Regression line 4 concepts

1. Fitting a least squares line and calculating the correlation coefficient

2. Interpolation and extrapolation of regression lines

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

4. Interpret the slope and intercept of a regression line

• #### Residuals 2 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

• #### Transforming to linearity 1 concept

1. Apply the correct quadratic, logarithmic or recipricol transformation and make predictions

### 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 Analysis

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

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