Classifying and Organising Data (Grade 12 NSC Matric Mathematical Literacy): Revision Notes
Classifying and Organising Data
Understanding data organisation and classification
Organising data means taking information and arranging it in a particular order, such as from smallest to largest or in alphabetical order. This makes the data much easier to read and understand.
Classifying data means grouping information into categories or classes based on shared characteristics. For example, you might group students by their exam performance levels or cars by their colours.
The purpose of organising and classifying data is to make patterns clearer and to help answer questions about the information more easily. This fundamental skill forms the basis for all statistical analysis and data interpretation.
Tally marks for counting discrete data
Tally marks provide a simple and effective way to count items when you're working with discrete data. Discrete data consists of separate, countable items like the number of cars sold, students in a class, or correct answers on a test.
How to draw tally marks correctly:
- Draw four vertical lines: ||||
- Cross them with a diagonal line for the fifth count: ||||/
- This creates groups of five, which are much easier to count quickly
- Start a new group of five after completing each set
Tally marks are especially useful when collecting data in real-time, such as during surveys, observations, or when counting responses.
Frequency tables
A frequency table displays how often each value or category appears in your dataset. It organises information into clear columns that show both the categories and how frequently each occurs.
Standard frequency table structure:
- Category column: Lists what you're counting (colours, age groups, etc.)
- Tally column: Shows tally marks for each category
- Frequency column: Gives the numerical count for each category
Worked examples
Worked Example 1: Creating a frequency table from organised data
An Audi sales representative has received cars in different colours. The complete data shows:
| Model | Red | White | Silver | Black |
|---|---|---|---|---|
| A3 | 2 | 5 | 4 | 3 |
| A4 | 3 | 2 | 3 | 6 |
| S3 | 4 | 3 | 5 | 5 |
| Q7 | 1 | 4 | 4 | 3 |
| R8 | 2 | 3 | 1 | 4 |
To create a frequency table specifically for A3 car colours:
| Colour | Frequency | Tally | ||||
|---|---|---|---|---|---|---|
| Red | 2 | |||||
| White | 5 | |||||
| Silver | 4 | |||||
| Black | 3 |
Step-by-step method:
- Extract the relevant data (A3 row only)
- List each category (colour) in the first column
- Count the frequency for each category from the original data
- Draw corresponding tally marks, ensuring every fifth mark crosses the previous four
Worked Example 2: Working with grouped frequency tables
When data covers a wide range of values, it's often grouped into intervals. This creates a grouped frequency table.
Consider seedling height measurements in millimetres:
| Height of seedling (mm) | Frequency |
|---|---|
| 10-14 | 3 |
| 15-19 | 6 |
| 20-24 | 7 |
| 25-29 | 5 |
| 30-34 | 4 |
Common question types and solutions:
a) How many plants were measured altogether? Add all frequencies: 3 + 6 + 7 + 5 + 4 = 25 plants
b) How many plants are less than 20 mm high? Include ranges below 20 mm: 3 + 6 = 9 plants
c) How many plants are more than 24 mm high? Include ranges above 24 mm: 5 + 4 = 9 plants
d) What percentage of seedlings are below 25 mm?
Plants below 25 mm: 3 + 6 + 7 = 16 plants
Percentage calculation:
e) How many plants are at least 25 mm high? Plants 25 mm or higher: 5 + 4 = 9 plants
Worked Example 3: Creating frequency tables from raw data
When given raw examination data, you need to organise it into meaningful performance categories. Geography exam marks (as percentages) can be grouped into seven performance levels:
| Performance Level | Percentage Range |
|---|---|
| 1 | 0 to 29 |
| 2 | 30 to 39 |
| 3 | 40 to 49 |
| 4 | 50 to 59 |
| 5 | 60 to 69 |
| 6 | 70 to 79 |
| 7 | 80 to 100 |
Method for processing raw data:
- Examine each individual score from the raw data
- Determine which performance level range it falls into
- Place a tally mark in the appropriate level's row
- Count all tally marks to determine the frequency for each level
- Verify that all frequencies sum to the total number of data points
Sample completed frequency table:
| Performance Level | Percentage Range | Tally | Frequency |
|---|---|---|---|
| 1 | 0–29 | 4 | |
| 2 | 30–39 | 5 | |
| 3 | 40–49 | 11 | |
| 4 | 50–59 | 8 | |
| 5 | 60–69 | 5 | |
| 6 | 70–79 | 8 | |
| 7 | 80–100 | 11 |
Total: 52 students
Essential exam strategies
Always verify your totals: The sum of all frequencies must equal the total number of data items. This catches calculation errors.
Read questions precisely: Pay close attention to key words:
- "More than" excludes the boundary value
- "Less than" excludes the boundary value
- "At least" includes the boundary value
- "At most" includes the boundary value
For percentage calculations: Use the formula
Tally mark accuracy: Every complete group should show exactly four vertical lines crossed by one diagonal line.
Working with grouped data: You can only use the ranges provided in the table, not individual values within those ranges.
Key Points to Remember:
- Organising data arranges information in order, while classifying data groups it by shared characteristics
- Tally marks use the pattern of four vertical lines crossed by a diagonal (||||/) to efficiently count discrete data in groups of five
- Frequency tables must include columns for categories, tallies, and numerical frequencies
- For grouped frequency tables, add frequencies from relevant ranges to answer specific questions
- Always check that your total frequencies match the original number of data points to verify accuracy