Final answer:
The peer group comparison statement is false because it does not require data to be displayed in a boxplot format. To evaluate the four true or false statements regarding a box plot, one must understand the components of a box plot, which includes the median, quartiles, and whiskers, and then examine the specific plot in question.
Step-by-step explanation:
True or False: A peer group comparison collects the returns produced by a representative universe of investors over a specific period of time and displays them in a simple boxplot format. This statement is false. A peer group comparison might include financial data such as returns, but it does not necessarily involve presenting the data in a boxplot format. A boxplot is a method of showing the distribution of a dataset that includes the median, quartiles, and outliers, which can be quite useful in statistical analysis to describe the central tendency and variability of the data.
Regarding the specific true or false statements based on a given box plot:
-
- A. The statement "Twenty-five percent of the data are at most five" can be true only if the first quartile (Q1) in the box plot is at most five.
-
- B. The statement "There is the same amount of data from 4-5 as there is from 5-7" is false if the box plot shows that the distances between these intervals represent different percentages of data points.
-
- C. The statement "There are no data values of three" is false if the number three is included in the whiskers, the box, or any part of the plot indicating it is a data point.
-
- D. The statement "Fifty percent of the data are four" is false unless both the second quartile (Q2 or median) and the third quartile (Q3) are at four, meaning the middle 50% of the data is at this value.
Understanding box plots is crucial in accurately interpreting the data they represent. The quartiles divide the data into four equal parts, and the whiskers show the range of the rest of the data, potentially excluding outliers. To determine the accuracy of statements A through D, we would need to examine Figure A2 and understand the components of the box plot.