Geometry, Measurement & Data
Understanding Data and Probability
Grade 4 · Grade 5 · Grade 6
- ✓By the end of this lesson students will be able to define and calculate the mean, median, and mode of a set of data.
- ✓By the end of this lesson students will be able to describe the likelihood of events using appropriate probability terms.
- ✓By the end of this lesson students will be able to express the probability of simple events as a fraction.
- ✓By the end of this lesson students will be able to collect, organize, and interpret simple sets of data.
Key concepts
Data is information, often in the form of numbers, that we collect about something. For example, the number of students who like apples, or the heights of all the students in your class.
The mean, also known as the average, is found by adding up all the numbers in a data set and then dividing by how many numbers there are. It tells us a typical value in the data.
The median is the middle number in a data set when the numbers are arranged in order from smallest to largest. If there are two middle numbers (when there's an even count of data), the median is the number exactly between them.
The mode is the number that appears most often in a data set. A data set can have one mode, more than one mode (if two or more numbers appear with the same highest frequency), or no mode (if all numbers appear only once).
Probability is the chance or likelihood that a specific event will happen. We can describe probability using words like 'impossible', 'unlikely', 'equally likely', 'likely', or 'certain'. We can also express it as a fraction.
These words help us describe how likely an event is:\n- Impossible: It will never happen (Probability = 0).\n- Unlikely: It probably won't happen, but it could.\n- Equally Likely: It has an even chance of happening or not happening (Probability = 1/2).\n- Likely: It probably will happen.\n- Certain: It will definitely happen (Probability = 1).
Key facts to remember
- 1The mean is the average: add all numbers and divide by how many there are.
- 2The median is the middle number after ordering the data.
- 3The mode is the number that appears most often.
- 4Always order your data from smallest to largest before finding the median.
- 5Probability is the chance of an event happening, often written as a fraction.
- 6Probability ranges from 0 (impossible) to 1 (certain).
- 7Likelihood terms help describe how probable an event is: impossible, unlikely, equally likely, likely, certain.
- 8A data set can have one mode, multiple modes, or no mode.
Worked examples
Example 1
A group of Grade 5 students recorded the number of books they read last month: 3, 5, 2, 8, 5, 4, 1. Find the mean, median, and mode of the number of books read.
Answer
Mean = 4 books\nMedian = 4 books\nMode = 5 books
Remember to always order the data first when finding the median!
Example 2
You have a bag with 3 red marbles, 2 blue marbles, and 5 yellow marbles. If you pick one marble without looking, what is the probability of picking a blue marble? Describe the likelihood.
Answer
The probability of picking a blue marble is 2/10 or 1/5. This event is 'unlikely'.
Always simplify your probability fractions to their lowest terms.
Example 3
Six students recorded their scores on a math quiz out of 10: 7, 9, 6, 8, 7, 10. Find the mean, median, and mode of their scores.
Answer
Mean ≈ 7.83\nMedian = 7.5\nMode = 7
When there's an even number of data points, the median is the average of the two middle numbers.
Common mistakes
- ✗Not ordering the data before finding the median, leading to an incorrect middle number.
- ✗Forgetting to divide by the correct number of data values when calculating the mean.
- ✗Confusing mean, median, and mode, or mixing up their definitions.
- ✗Not simplifying probability fractions to their lowest terms.
- ✗Incorrectly identifying the mode when there are multiple numbers with the same highest frequency, or stating there is no mode when there is one.
Exam tips
- ★Read the question carefully to know if you need to find the mean, median, mode, or probability.
- ★Show all your steps, especially for mean and median, so your teacher can see your thinking.
- ★When finding the median, cross off numbers from both ends of your ordered list until you reach the middle.
- ★For probability questions, clearly state the number of favourable outcomes and the total number of possible outcomes.
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