Statistics and probability accounts for 25-35% of LANTITE numeracy, making it one of the three major content areas alongside number and algebra (40-50%) and measurement and geometry (20-30%). The good news is that the content is clearly defined in the ACER Skills and Content Guide. Every topic that can appear on the test is listed. This post walks through each of them.
What the Skills Guide Lists for Statistics and Probability
According to the ACER Skills and Content Guide, the statistics and probability strand covers:
- Reading and interpreting graphs and data displays
- NAPLAN data
- Comparing data sets
- Sampling bias
- Box plots
- Mean, median, and mode
- Actual versus predicted scores
- Assigning grades from raw scores
- ATAR interpretation
- Probability
These topics appear in real-world contexts. The Skills Guide specifies three context categories: personal and community (45-55%), schools and teaching (30-40%), and further education (10-20%). Statistics questions will often use school-based scenarios: class results, NAPLAN reports, grade distributions, because that context fits a pre-service teacher audience.
Reading Graphs and Tables Under Time Pressure
Most statistics questions on LANTITE are not calculation-heavy. They test whether you can read a display accurately and draw a correct conclusion. Under the time constraints of the test (120 minutes, 65 questions across both sections), speed with data displays matters.
A reliable approach for any graph or table:
- Read the title first. Know what the display is showing before looking at values.
- Check the axes or column headers. Note units and scale.
- Read the question before studying the data in detail. This tells you what to look for.
- Identify the specific value or comparison the question asks about. Ignore the rest.
This approach applies equally to bar charts, line graphs, two-way tables, and box plots.
Box Plots
Box plots appear explicitly in the Skills Guide. A box plot displays five values: the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum. The box spans Q1 to Q3, which is the interquartile range (IQR). The line inside the box is the median.
| Feature | What It Shows | Common Question Type |
|---|---|---|
| Median line | Middle value of the data set | Compare medians between two groups |
| Box width (IQR) | Spread of the middle 50% of data | Which group has more consistent results? |
| Whisker length | Range of lower and upper 25% of data | Identify minimum, maximum, or range |
| Outlier dots | Values far outside the main distribution | Recognise unusual scores |
When comparing two box plots side by side (for example, two classes on the same assessment), focus on where the medians sit relative to each other and which box is wider. A wider box means more spread, not better performance.
Mean, Median, and Mode
These three measures of centre appear regularly. Know when each is appropriate:
- Mean: the arithmetic average. Sensitive to extreme values. A single very high or very low score pulls the mean toward it.
- Median: the middle value when data is ordered. Not affected by outliers. Often a better description of a typical score when the distribution is skewed.
- Mode: the most frequently occurring value. Most useful for categorical data or when identifying the most common score.
LANTITE questions in this area often ask you to identify which measure best represents a data set, or to calculate one from a small table of values. For the no-calculator section, calculations will involve small whole numbers and straightforward arithmetic.
NAPLAN Data and School Contexts
The Skills Guide specifically names NAPLAN data as a content area. Questions may present a NAPLAN-style report showing student results across bands, national averages, or year-level comparisons. You might be asked to:
- Identify how many students scored in a particular band
- Compare a school's result against a state or national average
- Determine whether a student's result is above or below the expected standard for their year
These questions do not require knowledge of specific real NAPLAN results. All values are given in the question. The skill being tested is accurate reading and interpretation.
Actual Versus Predicted Scores and Assigning Grades
Some questions present a scenario where predicted scores are compared to actual results, or where raw scores must be converted to grades using a provided scale. For grade-assignment questions, a conversion table is always given. Your task is to apply it correctly, including boundary cases (for example, where a score falls exactly on the cutoff between two grades).
ATAR Interpretation
The Skills Guide lists ATAR interpretation as a required skill. ATAR is a percentile rank, not a score out of 100. An ATAR of 80 means the student ranked above 80% of their eligible cohort. Questions in this area test whether you understand what a percentile rank represents and can apply that understanding to compare students or interpret admissions information.
Sampling Bias
Sampling bias occurs when the method of collecting data systematically favours certain outcomes or certain groups. A question might describe a survey method and ask whether the results can be generalised to the whole population. Common scenarios include surveys completed only by volunteers (self-selection bias) or samples drawn from a non-representative group.
Probability
Probability questions on LANTITE use straightforward scenarios: drawing from a set, selecting from a group, or interpreting a probability expressed as a fraction, decimal, or percentage. Key relationships to know:
- Probability values range from 0 (impossible) to 1 (certain).
- The probability of an event not occurring equals 1 minus the probability it does occur.
- For equally likely outcomes: probability = (number of favourable outcomes) divided by (total number of outcomes).
Calculator Section vs. No-Calculator Section
Statistics questions can appear in either section. Section 1 (52 questions, calculator permitted) is where complex calculations involving larger data sets will appear. Section 2 (13 questions, no calculator) will use small, clean numbers. If a statistics question appears in Section 2, expect values that work out to whole numbers or simple fractions. Once you move to Section 2, you cannot return to Section 1, so manage your time in Section 1 accordingly. ACER recommends spending 90-95 minutes on Section 1.
Practice LANTITE Numeracy Questions
Put these skills to the test with our LANTITE numeracy practice questions, including statistics and probability items across all difficulty levels.
START NUMERACY PRACTICEAll facts on this page are sourced directly from teacheredtest.acer.edu.au. For the latest information, always refer to the ACER website.