"Determine whether the data are qualitative or quantitative. Explain your reasoning.
Distances of track events"

Verified step by step guidance

1. Step 1: Understand the difference between qualitative and quantitative data. Qualitative data describes categories or qualities and is non-numerical, while quantitative data represents numerical values and measurements.
2. Step 2: Analyze the given data, 'Distances of track events.' Distances are numerical values that measure the length of track events, such as 100 meters, 200 meters, etc.
3. Step 3: Determine whether the data is numerical or categorical. Since distances are expressed in numbers and represent measurable quantities, they are numerical data.
4. Step 4: Conclude that the data is quantitative because it involves numerical measurements of distances, which can be used for mathematical operations like addition, subtraction, or averaging.
5. Step 5: Explain the reasoning: Quantitative data is used when the variable being measured is numerical and can be expressed in units, such as meters for track distances. This makes 'Distances of track events' a quantitative variable.

Key Concepts

Qualitative Data

Qualitative data refers to non-numerical information that describes characteristics or qualities. It is often categorical, meaning it can be divided into groups or categories based on attributes. Examples include colors, names, or types of events. Understanding whether data is qualitative helps in determining the appropriate statistical methods for analysis.

Quantitative Data

Quantitative data consists of numerical values that can be measured and expressed mathematically. This type of data can be further classified into discrete (countable) and continuous (measurable) data. Examples include heights, weights, and distances. Recognizing quantitative data is essential for applying statistical techniques such as mean, median, and standard deviation.

Data Classification

Data classification involves categorizing data into qualitative or quantitative types based on their characteristics. This classification is crucial for selecting the right analytical approach and statistical tests. For instance, knowing that distances of track events are quantitative allows for the use of various statistical methods to analyze trends, averages, and variability in the data.