Grade 9 Mathematics Unit 9 : Statistics and Probability

Numbers tell stories every day — exam results, rainfall, market prices, football scores — and this unit gives you the tools to read those stories with confidence. You’ll learn how to collect raw data, organise it in tables and graphs, pull out a single number that describes a whole group, and measure how spread out the values are. Then you’ll move from “what happened” to “what might happen” by studying probability: the mathematics of chance. By the end, you’ll be able to turn everyday observations into clear statistics and calculate the likelihood of real events.

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Chapter 9.1.1 – Collection and Tabulation of Statistical Data

Learn the first step of every statistical study: getting the data and putting it in order.

• Define statistics, population, sample, and variable in plain language
• Tell the difference between qualitative and quantitative data, and between discrete and continuous data
• Distinguish primary data (you collect it) from secondary data (someone else already collected it)
• Build a frequency distribution table from raw observations

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Chapter 9.1.2 – Graphical Presentations of Statistical Data

Turn numbers into pictures that anyone can read at a glance.

• Draw and interpret bar charts, line graphs, and pie charts
• Construct histograms from grouped frequency tables
• Choose the right graph type for a given data set
• Read information from a chart and explain what it shows

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Chapter 9.1.3 – Measures of Central Tendency

Find the “middle” of a data set using three different averages.

• Calculate the arithmetic mean for raw and grouped data
• Find the median for odd- and even-sized data sets
• Identify the mode and explain when it is most useful
• Compare mean, median, and mode and decide which one best describes a given situation

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Chapter 9.1.4 – Measures of Dispersion

Two classes can have the same average but very different scores — this chapter explains why.

• Calculate the range of a data set
• Compute variance (σ²) and standard deviation (σ) for raw and frequency data
• Explain what a large or small standard deviation tells you about the data
• Apply the effect of adding a constant or multiplying by a constant on variance and standard deviation

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Chapter 9.2 – Probability

Move from describing data to predicting outcomes using the mathematics of chance.

• Define experiment, outcome, sample space, and event using coins, dice, and card examples
• Distinguish experimental probability (from repeated trials) from theoretical probability (from counting)
• Calculate P(E) = (favourable outcomes) / (total outcomes) for single and combined experiments
• Use tree diagrams to list outcomes and find probabilities for two or three stage experiments (tossing coins, rolling dice, drawing balls)

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Learning Outcomes

By the end of this unit, you’ll be able to:

• Collect, classify, and tabulate statistical data from real situations
• Represent data using frequency tables, histograms, bar charts, and pie charts
• Calculate and compare mean, median, mode, range, variance, and standard deviation
• Define sample space and event, and list outcomes of simple experiments
• Calculate experimental and theoretical probabilities, including with tree diagrams
• Interpret statistical and probability results to make informed decisions in daily life