Final answer:
The statement is true because the full five-number summary is vital for describing the spread of a skewed distribution, providing details about the distribution that measures like the mean and standard deviation may not accurately represent.
Step-by-step explanation:
The statement that the best way to describe the spread of a skewed distribution is to report the full five-number summary is true. The five-number summary, which includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum, provides a comprehensive view of the data's distribution, especially when it is skewed.
It clearly shows the location of the median, the spread of the middle 50 percent of the data, and the extent of any outliers or skewness.
A box plot is a graphical representation of the five-number summary that can show the asymmetry or skewness in the distribution. For a distribution skewed to the right, there will be a larger gap between Q3 and the maximum compared to the gap between the minimum and Q1.
This representation helps in quickly identifying the skewness of a distribution. When distributions are not symmetric, the five-number summary gives more information than measures like the mean and standard deviation alone, which may be misleading in such cases. Hence, the spread of a skewed distribution is best described by its five-number summary.