Part A: Numeracy
7

Statistics & Data Interpretation

Interpret charts, graphs, averages, and statistics confidently

Learning Objectives

  • ✓ Calculate and compare mean, median, mode, and range
  • ✓ Read and interpret scatter plots, double-column graphs, and pie charts
  • ✓ Understand the impact of outliers on central tendency
  • ✓ Analyse student data tables and make comparisons
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Section 1: Types of Data and Tables

Data can be categorical (labels) or numerical (numbers). Tables are used to organize data into rows and columns for easy comparison.

Section 2: Calculating Mean, Median, Mode, and Range

Averages represent central data patterns. Mean is the sum divided by the count. Median is the middle value when sorted. Mode is the most frequent value. Range is the difference between highest and lowest.

Averages Quick Guide

AverageMethodProsCons
MeanSum / CountUses all data pointsSensitive to extreme outliers
MedianMiddle sorted valueNot affected by outliersTakes time to order large sets
ModeMost frequentEasy to identifyCan have multiple or no modes
Example 1

ACER Authentic Problem: Outlier Impact on Skewed Assessment Data (July 2017 Q24)

❓ Question: A teacher gives an assessment to 25 students. The mean score is 73.8%. Would the mean score be higher if the highest score (80%) and lowest score (63%) were both omitted?
📄 Source Passage / Reference Data:

SKEWED DATA

This graph shows a plot of the students’ scores. The mean of the scores is 73.8%.

Student Assessment Scores (%)

Class Size: 25 Students | Mean Score: 73.8%

60% 65% 70% 75% 80%
📝 Step-by-Step Method:
1
Calculate the total score sum for all 25 students.
2
Subtract the two omitted extreme scores (lowest 63% and highest 80%).
3
Divide the new sum by the remaining 23 students to find the new mean.
4
Compare the new mean (74.0%) with the original mean (73.8%).
🔍 Evidence Extracted: "New mean = 74.0%, which is higher than the original mean of 73.8%."
🎯 Final Answer: Yes (True)
💡 Why It Is Correct: The average of the two omitted scores is (63 + 80) ÷ 2 = 71.5%. Because 71.5% is lower than the cohort mean of 73.8%, removing these two scores eliminates more downward weight than upward weight, resulting in a higher overall mean.
⚡ LANTITE Exam Strategy: Official ACER Concept: Omitting values whose mean is below the overall average always pulls the remaining mean upward.
Example 2

ACER Authentic Problem: Interpreting Stacked Bar Charts (Sept 2023 Q5)

❓ Question: Was Engineering the STEM subject with the lowest percentage of students reporting they are 'Somewhat confident' or 'Very confident'
📄 Source Passage / Reference Data:

STEM CONFIDENCE

Survey of 2000 students aged 12–25 regarding confidence in getting good results.

STEM CONFIDENCE IN GETTING GOOD RESULTS

Survey of 2000 students aged 12–25 (Youth Insight Report 2019)

Not confident at all Not really confident Neither Somewhat Very confident Science 6% 11% 20% 39% 23% Technology 4% 9% 22% 41% 23% Engineering 11% 21% 31% 27% 10% Maths 8% 12% 18% 39% 23% 0% 25% 50% 75% 100%
📝 Step-by-Step Method:
1
Sum the 'Somewhat confident' and 'Very confident' bars for each subject.
2
Compare the totals.
🔍 Evidence Extracted: "Engineering total is 37%, the lowest of all four subjects."
🎯 Final Answer: Yes (True)
💡 Why It Is Correct: The combined confident categories for Engineering total 37%, which is visibly and numerically lower than Science (62%), Technology (64%), and Maths (62%).
⚡ LANTITE Exam Strategy: Visual Chart Reading: Combine adjacent stacked categories by adding their individual segmented percentages.

Section 4: Interpreting Sector (Pie) Graphs and Sector Percentages

Pie charts represent parts of a whole (100% or 360°). Each sector's size is proportional to the quantity it represents.

Section 5: Double Graphs and Scatter Plots

Double graphs compare two sets of data side-by-side. Scatter plots show the relationship (correlation) between two variables.

Question 1 of 10

ACER 2017 Q24: A class of 25 students has a mean test score of 73.8%. The highest score is 80% and lowest is 63%. If both are omitted, what happens to the mean?