Recap and sample data sets

Introduction

Information in the form of numbers, graphs and tables is all around us; on television, on the radio or in the newspaper. We are exposed to crime rates, sports results, rainfall, government spending, rate of HIV/AIDS infection, population growth and economic growth.

This chapter demonstrates how Mathematics can be used to manipulate data, to represent or misrepresent trends and patterns and to provide solutions that are directly applicable to the world around us.

Skills relating to the collection, organisation, display, analysis and interpretation of information that were introduced in earlier grades are developed further.

Recap of earlier work

The collection of data has been introduced in earlier grades as a method of obtaining answers to questions about the world around us. This work will be briefly reviewed.

Data and data collection

Data

Data

Data refers to the pieces of information that have been observed and recorded, from an experiment or a survey. There are two types of data: primary and secondary. The word "data" is the plural of the word "datum", and therefore one should say, "the data are" and not "the data is".

Data can be classified as primary or secondary , and primary or secondary data can be classified as qualitative or quantitative . [link] summarises the classifications of data.

• Primary data describes the original data that have been collected. This type of data is also known as raw data. Often the primary data set is very large and is therefore summarised or processed to extract meaningful information.
• Qualitative data is information that cannot be written as numbers, for example, if you were collecting data from people on how they feel or what their favourite colour is.
• Quantitative data is information that can be written as numbers, for example, if you were collecting data from people on their height or weight.
• Secondary data is primary data that has been summarised or processed, for example, the set of colours that people gave as favourite colours would be secondary data because it is a summary of responses.

Transforming primary data into secondary data through analysis, grouping or organisation into secondary data is the process of generating information.

Purpose of collecting primary data

Data is collected to provide answers that help with understanding a particular situation. Here are examples to illustrate some real world data collections scenarios in the categories of qualitative and quantitative data.

Qualitative data

• The local government might want to know how many residents have electricity and might ask the question: "Does your home have a safe, independent supply of electricity?"
• A supermarket manager might ask the question: “What flavours of soft drink should be stocked in my supermarket?" The question asked of customers might be “What is your favourite soft drink?” Based on the customers' responses, the manager can make an informed decision as to what soft drinks to stock.
• A company manufacturing medicines might ask “How effective is our pill at relieving a headache?” The question asked of people using the pill for a headache might be: “Does taking the pill relieve your headache?” Based on responses, the company learns how effective their product is.
• A motor car company might want to improve their customer service, and might ask their customers: “How can we improve our customer service?”