Recording raw data using tables and charts

Raw data is the initial, unprocessed information collected during research or observations. Recording this data in an organised manner allows researchers to make quick judgments in relation to hypotheses.

Tools for recording raw data

• Tally charts and frequency tables - These are simple tools used to count and record the frequency of occurrences for different categories.
• Summary tables - These consolidate raw data into a more compact form.

Example of a tally chart/frequency table

The table below shows the usage of mobile phones by students.

Representing numbers in standard and decimal form

Understanding standard form

• Definition - Standard form is a method to express very large or very small numbers by showing them as a product of a number between 1 and 10 and a power of 10.
• Purpose - It simplifies calculations and communication of numbers that are otherwise difficult to handle.
• Example - The number 45,000 can be written as $4.5\times {10}^4$, meaning 4.5 multiplied by 10 four times (or 10,000).

Understanding decimal form

• Definition - Decimal form represents parts of a whole number, typically values less than 1, using a decimal point followed by digits.

Simplifying numbers using significant figures

When dealing with complex or lengthy numbers, simplifying them to a manageable form is often necessary. Significant figures provide a way to round numbers while maintaining their approximate value.

Rules for significant figures

• Purpose - Significant figures reduce the complexity of numbers by rounding them to a specified number of digits.
• Rounding rule - If the digit following the last significant figure is 5 or higher, round up; if it is 4 or lower, leave it as is.
• Examples:
  • The number 6640 rounded to one significant figure becomes 7000 (since the next digit is 5 or more).
  • The number 0.0536 rounded to one significant figure becomes 0.05 (since the next digit is less than 5).
  • To two significant figures, 6640 becomes 6600, and 0.0536 becomes 0.054.
• Importance of the first digit - The first digit carries the most weight as it indicates the general magnitude of the number, making it the most significant.

Making estimations from collected data

Estimations are an essential skill in data analysis, allowing for quick approximations when exact values are not necessary or immediately available.

Principles of data estimation

• Definition - Estimation involves determining a value that is close to the actual figure, usually with some thought or basic calculation involved.