The modified box plot helps analyze data distribution. While statements a, c, d, and g hold true based on the information provided, statements b, e, and f are incorrect due to misinterpretations of whisker and outlier boundaries.
a. True: The range is indeed the difference between the highest and lowest values, which in this case is r - y.
b. False: The statement claims 25% of the scores are at or below y. However, the boxplot shows y as the lower whisker, which represents potential outliers, not the first quartile (Q1). Therefore, only a small fraction of the data points, likely less than 5%, are below y.
c. True: The interquartile range (IQR) is the difference between the third and first quartiles, represented by u - z in the statement and the box's width in the graph.
d. True: The median is the middle value of the data, represented by w and the line dividing the box in the graph.
e. False: The statement incorrectly claims r as the lower outlier boundary. The actual boundary is typically defined as Q1 - 1.5*IQR, which is likely below y in this case.
f. False: Similar to statement e, the upper outlier boundary is not y but Q3 + 1.5*IQR, which is likely above u in this case.
g. True: The statement accurately describes the interquartile range. 50% of the data points fall between Q1 (z) and Q3 (u), represented by the box in the graph.