Determine the level of measurement of the data set. Explain.
The total compensations (in millions of dollars) of the ten highest-paid CEOs at U.S. public companies are listed. (Source: 24/7 Wall St.)
280.6 66.9 42.9 36.5 34.3 31.6 31.6 28.8 26.4 25.8

Verified step by step guidance

1. Identify the four levels of measurement in statistics: nominal, ordinal, interval, and ratio. Each level represents a different way of categorizing and interpreting data.
2. Examine the data set provided: 280.6, 66.9, 42.9, 36.5, 34.3, 31.6, 31.6, 28.8, 26.4, 25.8. These are numerical values representing the total compensations of CEOs in millions of dollars.
3. Determine if the data has a true zero point. In this case, a compensation of \$0 would indicate the absence of compensation, which confirms the presence of a true zero point.
4. Assess whether the data can be meaningfully compared using ratios. For example, a compensation of \$280.6 million is 10 times greater than \$28.8 million, which is a valid ratio comparison. This confirms that the data is at the ratio level of measurement.
5. Conclude that the level of measurement for this data set is 'ratio' because it is numerical, has a true zero point, and allows for meaningful ratio comparisons.

Key Concepts

Levels of Measurement

Levels of measurement refer to the different ways data can be categorized and quantified. There are four primary levels: nominal, ordinal, interval, and ratio. Each level has distinct characteristics, with ratio being the highest level, allowing for meaningful comparisons and calculations, including the use of absolute zero.

Ratio Level Data

Ratio level data is a type of quantitative data that possesses all the properties of interval data, but also includes a true zero point, which allows for the comparison of absolute magnitudes. In the context of the CEO compensation data, the total compensations can be compared, and a value of zero would indicate no compensation, making it a ratio level measurement.

Descriptive Statistics

Descriptive statistics involve summarizing and organizing data to understand its main features. This includes measures such as mean, median, and mode, which can provide insights into the central tendency of the compensation figures. Understanding these statistics is essential for interpreting the data set effectively.