Learning Objectives
- Collect and organize data
- Calculate mean, median, and mode of a data set
- Represent data using bar graphs and double bar graphs
- Understand probability as a measure of chance
Key Concepts
Mean (Average)
Mean = Sum of all observations ÷ Number of observations
Example: Mean of 4, 6, 8, 10, 12 = (4+6+8+10+12)/5 = 40/5 = 8
Median
The middle value when data is arranged in ascending or descending order.
For odd number of values: median is the middle value.
For even number of values: median is the average of the two middle values.
Mode
The value that occurs most frequently in the data set.
A data set can have more than one mode (bimodal, multimodal) or no mode at all.
Bar Graphs and Double Bar Graphs
Bar graphs use bars of uniform width to represent data. Double bar graphs compare two sets of data side by side.
Probability
Probability = Number of favourable outcomes ÷ Total number of outcomes
Probability always lies between 0 and 1. P = 0 means impossible, P = 1 means certain.
Summary
Data handling involves collecting, organizing, and interpreting data. Mean, median, and mode are measures of central tendency. Bar graphs provide visual representation. Probability measures the chance of an event occurring.
Important Terms
- Mean
- The average value of a data set, calculated by dividing the sum by count
- Median
- The middle value in an ordered data set
- Mode
- The most frequently occurring value in a data set
- Range
- The difference between the highest and lowest values
- Probability
- A measure of the likelihood of an event, expressed as a number between 0 and 1
Quick Revision
- Mean = Sum of observations / Number of observations
- Arrange data in order before finding median
- Mode is the most frequent value
- Range = Maximum value - Minimum value
- Probability of an event = Favourable outcomes / Total outcomes
Practice Tips
- Collect real data (marks, heights, temperatures) and find mean, median, mode
- Draw bar graphs for data you collect from your class
- Use coins and dice to understand experimental probability