Final answer:
In a box-and-whisker plot, the median divides the data into two equal parts, with half the data below and half above this value. If the median is given as 6, then the correct description of the data set is that half of the data is less than 6 and half is greater than 6.
Step-by-step explanation:
Understanding Box-and-Whisker Plots
A box-and-whisker plot, or box plot, displays the distribution of a set of data. It is especially useful for showing the median, quartiles, and range of the data. The median divides the data into two equal halves. The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) represents the median of the upper half, effectively splitting the entire data set into quarters.
In a box plot, the box itself contains the middle 50 percent of the data, which is also known as the interquartile range (IQR). The whiskers extend from the ends of the box to the smallest and largest data values, showing the full range of the data set.
Returning to the original question about the median value in a box-and-whisker plot, by definition the median represents the center of the data set, with half of the data points lying below this value and half lying above. Therefore, the correct statement that describes a box-and-whisker plot with a median of 6 would be:
Half of the data is less than 6, and half of the data is greater than 6.
This corresponds to option B from the initial options presented to us.