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Introduction to Statistics & Probability – Functional Skills Maths Level 2

Statistics and probability help us make sense of data and understand the likelihood of events happening. These skills are useful in everyday life, such as analyzing trends, making predictions, and making informed decisions.

1. Understanding Statistics

What is Statistics?

Statistics is the study of collecting, organizing, analyzing, and interpreting data. It helps us identify patterns and make decisions based on facts.

Types of Data:

📌 Qualitative data – Descriptive information (e.g., colors, opinions, types of pets).
📌 Quantitative data – Numerical information (e.g., height, weight, test scores).

Discrete data: Whole numbers only (e.g., number of students).

Continuous data: Can have decimals (e.g., weight, temperature).

Presenting Data

Data can be displayed in different formats, including:
✔ Tables – Organizes numerical data for easy comparison.
✔ Bar charts – Uses bars to represent quantities (good for categories).
✔ Pie charts – Shows proportions of a whole (good for percentages).
✔ Line graphs – Displays trends over time.
✔ Histograms – Similar to bar charts but for continuous data (no gaps between bars).

Measures of Central Tendency (Averages)

Averages help summarize data into a single value. The three main types are:

1️⃣ Mean – The sum of all values divided by the number of values.

Example: The test scores are 5, 7, 8, 10.

Mean = (5 + 7 + 8 + 10) ÷ 4 = 7.5

2️⃣ Median – The middle value when numbers are in order.

Example: The numbers are 3, 5, 7, 9, 11. The median is 7.

3️⃣ Mode – The most frequently occurring number.

Example: In 2, 3, 3, 5, 7, the mode is 3 (it appears twice).

📌 Tip:

Use mean for a general average.

Use median when there are extreme values (outliers).

Use mode when looking for the most common value.

2. Understanding Probability

What is Probability?

Probability measures how likely an event is to happen. It is written as a fraction, decimal, or percentage between 0 and 1.

📌 Probability scale:

0 = Impossible (e.g., rolling a 7 on a standard die).

0.5 = Even chance (e.g., flipping a coin).

1 = Certain (e.g., the sun rising tomorrow).

Calculating Probability

The probability of an event happening is:

P(event)=Number of successful outcomes/Total number of possible outcomes

👉 Example: What is the probability of rolling a 4 on a fair six-sided die?

There is 1 way to roll a 4.

There are 6 possible outcomes (1, 2, 3, 4, 5, 6).

Probability = 1/6 or 0.1667 (16.67%).

Probability with Two Events

For independent events (one event does not affect the other), multiply the probabilities.

👉 Example: What is the probability of flipping two heads in a row?

Probability of one head = 1/2

Probability of two heads = 1/2 × 1/2 = 1/4 (25%)

For dependent events (one event affects another), adjust the probability after each event.

👉 Example: A bag contains 3 red and 2 blue balls. If you take one ball and don’t put it back, what is the probability of drawing two red balls?

First red ball: 3/5

Second red ball (after one red is removed): 2/4

Probability = 3/5 × 2/4 = 6/20 = 3/10 (30%)

Expected Outcomes

Expected outcomes predict how often an event will happen over many trials.

Expected outcomes=Probability×Number of trials

👉 Example: If you roll a die 60 times, how many times do you expect to roll a 6?

Probability of rolling a 6 = 1/6

Expected times = (1/6) × 60 = 10 times

Key Skills to Practice

✔ Reading and interpreting charts, tables, and graphs.
✔ Calculating mean, median, and mode.
✔ Finding probabilities and expected outcomes.
✔ Understanding independent and dependent events.

Would you like some practice questions? 😊

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A two-way table is a way of organizing data that involves two categories. It helps compare information and identify relationships between different groups.

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A tree diagram is a visual way to show all possible outcomes of an event. It is especially useful in probability when dealing with multiple events, such as flipping a coin twice or picking two cards from a deck.

Why Use a Tree Diagram?

✔ Helps organize possible outcomes clearly.
✔ Makes it easy to calculate probabilities for multiple events.
✔ Useful for independent and dependent probability problems.

How to Draw a Tree Diagram

A tree diagram consists of branches that represent different outcomes. Each branch is labeled with a probability.

👉 Example: Flipping a Coin Twice
If you flip a coin twice, the possible outcomes are:

1️⃣ First flip: Heads (H) or Tails (T)
2️⃣ Second flip: Heads (H) or Tails (T)