Learning Objectives
- Organise data using frequency distribution tables
- Construct and interpret bar graphs, histograms, and pie charts
- Understand grouped and ungrouped frequency distributions
- Learn the basics of probability
Key Concepts
Organising Data
Raw data can be organised using tally marks and frequency distribution tables. Frequency is the number of times a particular value occurs. For large data sets, data is grouped into class intervals (e.g., 0-10, 10-20, etc.).
Grouped Frequency Distribution
When data has a wide range, we group it into class intervals. Each class interval has a lower limit and an upper limit. The class size = upper limit - lower limit. The class intervals should be continuous (no gaps).
Histogram
A histogram is a bar graph that represents a grouped frequency distribution. The bars are drawn with no gaps between them. The x-axis shows class intervals and the y-axis shows frequency. Unlike bar graphs, histograms represent continuous data.
Pie Chart (Circle Graph)
A pie chart shows data as parts of a circle. The total angle at the centre is 360°. The central angle for each category = (value of the category / total value) × 360°. Each sector represents a proportion of the whole.
Probability
Probability measures the chance of an event occurring. Probability of an event = Number of favourable outcomes / Total number of outcomes. Probability always lies between 0 and 1 (inclusive). A probability of 0 means the event is impossible; a probability of 1 means the event is certain.
Random Experiment: An experiment whose outcome cannot be predicted in advance (e.g., tossing a coin, rolling a die).
Summary
Data handling involves collecting, organising, and interpreting data. Frequency distribution tables organise data efficiently. Histograms display grouped data, while pie charts show proportions. Probability quantifies the likelihood of events and ranges from 0 to 1.
Important Terms
- Data: Collection of numbers or information gathered for analysis
- Frequency: The number of times a particular observation occurs
- Class Interval: A range of values used to group data
- Histogram: A bar chart for grouped continuous data with no gaps
- Pie Chart: A circular chart divided into sectors representing proportions
- Probability: A measure of the chance that an event will occur
Quick Revision
- Frequency = count of each data value or group
- Histogram: bars touch (continuous data); Bar graph: bars separated (discrete data)
- Pie chart central angle = (value / total) × 360°
- Probability = favourable outcomes / total outcomes
- 0 ≤ Probability ≤ 1
- Sum of all probabilities of all outcomes = 1