Final answer:
When a median divides the box plot into two unequal sections, it reflects an asymmetric distribution of data, indicating skewness. A wider box, or a greater distance between Q1 and Q3, suggests a larger variability in the middle 50 percent of the data set. Outliers are identified using the interquartile range (IQR) and the 1.5(IQR) rule.
Step-by-step explanation:
A box plot is a graphical representation used to show the distribution of numerical data through their quartiles, including the median. The question revolves around the scenario when a median divides the box into two unequal pieces, which indicates that the data may not be symmetrically distributed around the median. When constructing a box plot, the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value are the key components.
In cases where the median is the same as Q3, the box plot would not have a median line inside the box; the right side of the box would represent both median and Q3. If the median divides the box into two unequal pieces, it implies the data is skewed. For example, if Q1 equals the smallest value, and the median is closer to Q1 than to Q3, it suggests a right-skewed distribution. On the contrary, if the median is closer to Q3, it indicates a left-skewed distribution. Moreover, the interquartile range (IQR), which is the distance between Q1 and Q3, represents the middle 50 percent of the data and shows the spread of the central portion of the dataset.
Thus, when comparing two box plots, the one with a wider spread between Q1 and Q3 indicates greater variability within the middle 50 percent of the data. It is essential to consider the potential for outliers, which are values that lie below Q1 − 1.5(IQR) or above Q3 + 1.5(IQR).