Final answer:
Variance (option c) is not measured in the same units as the original variable itself; it is measured in the units squared. In contrast, inner quartile range (IQR), mean, and median are measured in the original units of the data.
Step-by-step explanation:
The student is asking about different statistical measures and which one is not measured in the same units as the original variable. The correct answer to this question is variance. Unlike the other measures listed—inner quartile range (IQR), mean, and median—variance is measured in the units of the original variable squared. For example, if the original data is measured in dollars, the variance will be measured in dollars squared.
The first quartile (Q1) is the median of the lower half of the data, while the third quartile (Q3) marks the median of the upper half. The median splits the data into two equal parts. The interquartile range is the difference between the third and the first quartile (IQR = Q3 - Q1), and it represents the spread of the middle 50 percent of the data. This IQR is measured in the original units of the data, just like the mean and median are.
Understanding the interquartile range is important for identifying outliers and understanding the dispersion of the data set. It helps to compare data across different samples. In contrast, variance is a measure of how widely the points in a data set are spread out around the mean, and because it is squared, it is not in the original data units.