"Determine whether the data are qualitative or quantitative, and determine the level of measurement of the data set.
The numbers of performances for the 10 longest-running original runs of Broadway shows as of March 15, 2020, are listed. (Source: Playbill)
13,370 9692 9302 7485 6836 6680 6137 5959 5758 5461"

Verified step by step guidance

1. Step 1: Understand the distinction between qualitative and quantitative data. Qualitative data describes categories or qualities, while quantitative data represents numerical values that can be measured or counted.
2. Step 2: Examine the data set provided: 13,370, 9692, 9302, 7485, 6836, 6680, 6137, 5959, 5758, 5461. These are numerical values representing the number of performances, which makes the data quantitative.
3. Step 3: Determine the level of measurement. Quantitative data can be classified as either interval or ratio level. Ratio level data has a meaningful zero point, allowing for comparisons such as 'twice as many.'
4. Step 4: Since the number of performances has a meaningful zero (zero performances indicate no performances), the data is at the ratio level of measurement.
5. Step 5: Summarize: The data are quantitative and are measured at the ratio level.

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. In the context of the question, the performances of Broadway shows are numerical, indicating that the data is quantitative.

Levels of Measurement

Levels of measurement categorize data based on the nature of the information they represent. There are four levels: nominal, ordinal, interval, and ratio. The data in the question, which consists of counts of performances, is at the ratio level because it has a true zero point (no performances) and allows for meaningful comparisons and calculations.

Descriptive Statistics

Descriptive statistics summarize and describe the main features of a data set, providing simple summaries about the sample and measures. This includes measures such as mean, median, mode, and range. Understanding descriptive statistics is essential for interpreting the performance data of Broadway shows, as it helps to convey the overall trends and patterns within the data.