Probability & Statistics Basics
Probability and statistics provide methods for collecting, summarising, and interpreting data alongside calculating the likelihood of events. Key GCSE topics include averages from frequency tables, cumulative frequency and box plots, histograms, Venn diagrams, and probability tree diagrams for independent and conditional events.
- Mean
- The sum of all values divided by the number of values.
- Median
- The middle value when data is arranged in numerical order.
- Mode
- The most frequently occurring value in a data set.
Quadratic Parabola Plotter, Roots, Turning Point & Quadratic Formula
Adjust coefficients a, b, and c in y = ax² + bx + c to see how the parabola, roots (x-intercepts), and turning point move on the graph.
y = x² - 2x - 3
(-2)² − 4(1)(-3) = 16 → 2 real roots (crosses x-axis twice)x = 1.00b in brackets when squaring: (-2)² = 4 (always positive!). Typing -2² into a calculator without brackets gives -4 and loses the accuracy mark.Key Concepts & Exam Definitions (5)
- Mean
- The sum of all values divided by the number of values.
- Median
- The middle value when data is arranged in numerical order.
- Mode
- The most frequently occurring value in a data set.
- Independent Event
- An event where the outcome is not influenced by previous events.
- Venn Diagram
- A diagram using overlapping circles to represent the mathematical or logical sets of data.
Quick-Fire Flashcards (5)
Click any card to check the answer, then mark it as Known to track your progress.
What is the probability of an event that is certain to happen?
How do you calculate the range of a data set?
In a tree diagram, what do you do with probabilities along the branches?
What do all mutually exclusive outcomes of an event add up to?
Which average can be used for categorical (non-numerical) data?
Exam-Style Questions & Mark Schemes (3)
Write or think through your answer first, then click Check Mark Scheme to see the exact points examiners award marks for.
- Q1
Find the mean of the numbers 4, 7, 2, 9, 8.
Click “Check Mark Scheme” to compare your answer, 6. (4+7+2+9+8) = 30. 30 / 5 = 6.
- Q2
A bag contains 3 red balls and 2 blue balls. A ball is drawn at random. What is the probability it is blue?
Click “Check Mark Scheme” to compare your answer, 2/5
- Q3
The probability of rain tomorrow is 0.3. What is the probability that it does not rain?
Click “Check Mark Scheme” to compare your answer, 0.7 (1 - 0.3)
Common Exam Questions (3)
What is the difference between mutually exclusive and independent events?
Mutually exclusive events cannot happen at the same time, so P(A or B) = P(A) + P(B). Independent events do not affect the probability of each other occurring, so P(A and B) = P(A) × P(B).
How do you find the median from a grouped frequency table?
Find the position of the median using n ÷ 2 (or (n + 1) ÷ 2 for discrete data), then add the frequencies down the table (cumulative frequency) to identify which class interval contains that middle value.
When should I use a tree diagram?
Use a probability tree diagram when modelling two or more successive trials, particularly when probabilities change on the second branch (conditional probability without replacement).
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