Data & Probability
Learn to calculate mean, median and mode, read data displays, and compare experimental results with theoretical probability.
Mean, Median & Mode
These are three ways to describe the "average" or "typical" value in a set of data.
Mean
Add all the values, then divide by how many values there are.
The "fair share" average.
Median
The middle value when data is arranged in order.
If even number of values, average the two middle ones.
Mode
The value that appears most often.
There can be more than one mode, or none.
Example: Test Scores
Scores: 4, 7, 5, 7, 3, 8, 7
Mean: (4 + 7 + 5 + 7 + 3 + 8 + 7) ÷ 7 = 41 ÷ 7 = 5.86 (approx.)
Median: Order the data: 3, 4, 5, 7, 7, 7, 8. The middle value is 7.
Mode: 7 appears 3 times (more than any other). Mode = 7.
Reading Data Displays
Column Graph: Favourite Sports
The tallest bar shows the most popular sport (Soccer = 12 votes).
Total students: 12 + 8 + 6 + 10 + 4 = 40
Dot Plot: Number of Books Read
Number of books read this month
Each dot = 1 student. The mode is 2 books (tallest column of dots).
Experimental vs Theoretical Probability
Theoretical Probability
What we expect to happen based on maths.
P(Heads) = 1/2 = 0.5 (50%)
Experimental Probability
What actually happens when we do the experiment.
If we flip 20 times and get 12 Heads: 12/20 = 0.6 (60%)
Example: Rolling a Die 30 Times
| Number | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Theoretical (expected) | 5 | 5 | 5 | 5 | 5 | 5 |
| Experimental (actual) | 4 | 6 | 3 | 7 | 5 | 5 |
The experimental results are close to but not exactly the theoretical prediction. With more trials, they tend to get closer. This is called the Law of Large Numbers.
Key Vocabulary
Mean
The sum of all values divided by the count. Also called the average.
Median
The middle value when data is sorted from smallest to largest.
Mode
The value that occurs most frequently in a data set.
Data
Information collected through observations, surveys, or experiments.
Worked Examples
Find the mean of: 6, 8, 10, 4, 12
Step 1: Add all values: 6 + 8 + 10 + 4 + 12 = 40
Step 2: Count the values: 5
Step 3: Divide: 40 ÷ 5 = 8
Find the median of: 3, 9, 1, 7, 5
Step 1: Order the data: 1, 3, 5, 7, 9
Step 2: Find the middle value (3rd of 5 values).
Answer: Median = 5
Find the mode of: 2, 5, 3, 5, 8, 5, 3
Step 1: Count how often each appears: 2(1), 3(2), 5(3), 8(1)
Answer: 5 appears most often. Mode = 5
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the mean of: 5, 10, 15, 10?
Question 2
What is the median of: 12, 3, 7, 9, 5?
Question 3
What is the mode of: 4, 6, 4, 8, 6, 4, 9?
Question 4
A spinner was spun 50 times. It landed on red 20 times. What is the experimental probability of landing on red?
Question 5
Use the column graph below. How many more students chose Soccer than Tennis?
Key Concepts Summary
- ●Mean = total of all values ÷ number of values.
- ●Median = middle value when data is sorted.
- ●Mode = most frequent value.
- ●Theoretical probability is what we expect; experimental probability is what actually happens.
- ●The more trials in an experiment, the closer experimental results get to theoretical predictions.