Determine whether the data are qualitative or quantitative, and determine the level of measurement of the data set.
The top six final scores at the 2021 U.S. Women’s Figure Skating Championships are listed. (Source: NBC Sports)
232.61 215.33 214.98 213.39 199.95 178.89

Verified step by step guidance

1. Step 1: Understand the difference between qualitative and quantitative data. Qualitative data describes categories or qualities (e.g., colors, names), while quantitative data represents numerical values that can be measured or counted (e.g., scores, heights). In this case, the data consists of numerical scores, so it is quantitative.
2. Step 2: Review the four levels of measurement: nominal, ordinal, interval, and ratio. Nominal data categorizes without a specific order, ordinal data has a meaningful order but no consistent difference between values, interval data has consistent differences but no true zero, and ratio data has consistent differences and a true zero.
3. Step 3: Analyze the data set. The scores represent measurable quantities with meaningful differences between values (e.g., the difference between 232.61 and 215.33 is meaningful). Additionally, the scores have a true zero point (a score of 0 would indicate no performance), which makes the data at the ratio level of measurement.
4. Step 4: Conclude that the data are quantitative because they are numerical and measurable, and the level of measurement is ratio because the data have meaningful differences and a true zero point.
5. Step 5: To summarize, the data set consists of quantitative data at the ratio level of measurement, as the scores are numerical, measurable, and have a true zero point.

Key Concepts

Qualitative vs. Quantitative Data

Qualitative data refers to non-numerical information that describes characteristics or qualities, such as names or categories. In contrast, quantitative data consists of numerical values that can be measured and analyzed statistically. Understanding the distinction is crucial for determining how to interpret and analyze the data set effectively.

Levels of Measurement

The levels of measurement categorize data based on the nature of the information they represent. There are four levels: nominal, ordinal, interval, and ratio. Each level has different properties and implications for statistical analysis, with ratio being the highest level, allowing for a true zero point and meaningful comparisons between values.

Descriptive Statistics

Descriptive statistics summarize and describe the main features of a data set, providing insights into its central tendency, variability, and overall distribution. Common measures include mean, median, mode, and standard deviation. This concept is essential for interpreting the final scores in the context of the competition and understanding their significance.