Question

Arrange the box plots in order of least to greatest variability. Is "variability" represented by the IQR (Interquartile Range)?

A. Yes, IQR represents variability.
B. No, IQR does not represent variability.
C. No, variability is represented by the range.
D. Yes, variability is represented by the standard deviation.

Answer 1

The Interquartile Range (IQR) measures variability within a dataset, representing the spread of the middle 50 percent. Box plots are arranged by the width of the IQR when comparing variability. The correct answer is A. Yes, IQR represents variability.

Step-by-step explanation:

Yes, the Interquartile Range (IQR) represents variability within a dataset.

The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1), and it illustrates the spread of the middle 50 percent of the data.

A larger IQR indicates greater variability amongst the middle range of the data.

When arranging box plots by variability, you should look at the width of the IQR.

A larger width indicates greater variability, as it represents a wider spread of the middle 50 percent of the scores.

To construct a box plot, one marks the smallest value, the first quartile, the median, the third quartile, and the largest value on a number line, with a box covering the range from Q1 to Q3 and whiskers extending to the smallest and largest values.

Therefore, the correct answer is A. Yes, IQR represents variability.