Final answer:
The ages (in years) of students represent a ratio level of measurement because we can order the ages, calculate the difference and ratio between them, and there is a true zero point (birth). Therefore, the correct level of measurement for the given data set is ratio, option d.
Step-by-step explanation:
Determining the level of measurement for a data set involving the ages (in years) of 6 students in a high school is essential for choosing the correct statistical procedures. The ages of the students being {15, 15, 17, 17, 17, 18} can be organized and analyzed depending on what type of measurement scale they fall under. The four levels of measurement in statistics are nominal, ordinal, interval, and ratio, each with increasing order of information provided.
A nominal scale is used for categorical data that cannot be ordered nor used in calculations. An ordinal scale allows for ordering but does not support the measurement of differences between data points. An interval scale provides a definitive ordering and allows for the measurement of differences between data points, but does not have a true zero point. Lastly, a ratio scale carries all the properties of an interval scale, but also has a true zero point, allowing for the calculation of ratios.
In the case of the ages of 6 students, we can order the ages, calculate the difference between ages, and also calculate ratios (e.g., one student could be twice as old as another if their ages were, say, 4 and 8 years). Therefore, the measurement level for the ages of students is ratio. This is due to the fact that age has a true zero point (birth), and we can make meaningful comparisons using ratios, such as one age being twice another. Hence, the correct option for the data set given is d. ratio.