HSC Mathematics Standard 2 topic guide

Statistical Analysis

Statistical Analysis is a core part of HSC Mathematics Standard 2. This guide connects the syllabus ideas behind Data Analysis, Relative Frequency and Probability, Bivariate Data Analysis, The Normal Distribution, shows how they appear in worked problems, and points you to the formulas and full lessons needed for exam revision.

What you will learn

Statistical Analysis syllabus outline

The units below follow the structure used in the full Study to Learn course. Use the outline to identify exactly which idea needs attention, then work through the public example before continuing to the complete lesson path.

D.1

Data Analysis

Measures of Central Tendency and Spread · Standard Deviation

D.2

Relative Frequency and Probability

Probability and Relative Frequency

D.3

Bivariate Data Analysis

Scatterplots and Correlation · Line of Best Fit

D.4

The Normal Distribution

z-Scores and the Empirical Rule

Free worked preview

Measures of Central Tendency and Spread

This complete preview comes from the Data Analysis unit. It introduces the core language, shows the method in context, and gives you a real example of the lesson quality before you create an account.

Central Tendency and Spread, Revisited

Mean xˉ=∑xinor, for frequency data: xˉ=∑fixi∑fi\text{Mean } \bar{x} = \frac{\sum x_i}{n} \quad \text{or, for frequency data: } \quad \bar{x}=\frac{\sum f_ix_i}{\sum f_i}
Quartiles and the Interquartile Range

Q1 (lower quartile), Q2 (the median), Q3 (upper quartile) divide ordered data into quarters.

IQR=Q3−Q1IQR = Q_3 - Q_1

IQR is less sensitive to outliers than the range, since it ignores the extreme 25% at each end.

Common ErrorFor grouped/frequency data, use the class midpoint as x_i in the mean formula — not the class boundary.
Worked Example Find Q1, the median, and Q3 for: 3, 7, 8, 12, 14, 18, 21, 25 (already ordered, 8 values).
1Average the two middle values of the full ordered data setMedian=12+142\text{Median} = \frac{12+14}{2}
2Simplify (12+14)/2Median=13\text{Median} = 13
3The 4 values below the medianLower half: 3,7,8,12\text{Lower half: } 3,7,8,12
4Q1 is the median of the lower half — average its two middle valuesQ1=7+82Q_1=\frac{7+8}{2}
5Simplify (7+8)/2Q1=7.5Q_1=7.5
6The 4 values above the medianUpper half: 14,18,21,25\text{Upper half: } 14,18,21,25
7Q3 is the median of the upper half — average its two middle valuesQ3=18+212Q_3=\frac{18+21}{2}
8Simplify (18+21)/2Q3=19.5Q_3=19.5
9Subtract Q1 from Q3IQR=19.5−7.5IQR = 19.5-7.5
IQR=12IQR = 12
Practice QuestionFind the IQR of: 5, 9, 11, 14, 17, 20, 24, 29.

Use the formulas

Keep the formula sheet beside you

Revision becomes faster when you practise locating the right equation and understand what every variable means. The full reference is public and searchable on any device.

Open HSC Mathematics Standard 2 Formula Sheet →

Reviewed by the Study to Learn editorial team · Updated 2026-07-24