Final answer:
A box plot represents data distribution with a five-number summary. To confirm truthfulness of statements about a dataset, one must know the values of these summary points. Interpreting a box plot requires an understanding of quartiles, median, minimum, and maximum.
Step-by-step explanation:
To understand box plots and interpret the data they represent, it's important to review their basic components. A box plot, also known as a whisker diagram, shows the distribution of data based on a five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
Let's address the provided statements:
- A. Twenty-five percent of the data are at most five. Since Q1 represents the 25th percentile of the data, this statement is true only if Q1 is at or below five on the box plot.
- B. There is the same amount of data from 4-5 as there is from 5-7. This would be true if the box (which represents the interquartile range) extends from 4 to 5, and one whisker extends from 5 to 7. However, the equality of data points within these ranges depends on how the actual data points are distributed, which is not provided in a box plot.
- C. There are no data values of three. This statement would only be true if the minimum value on the box plot is greater than three.
- D. Fifty percent of the data are four. This statement can be true only if both the median and Q1 (or Q3) are at exactly four.
For constructing a box plot (e), one would gather the dataset, calculate Q1, median, Q3, the minimum, and the maximum and then draw a box from Q1 to Q3 with a line inside it marking the median. Whiskers are then drawn from the box to the minimum and maximum values. The middle 50 percent of the weights (f) are represented by the range between Q1 and Q3.
In regards to (g and h), if the data represents a subset of the whole population such as professional football players, the data would be considered a sample. On the other hand, if the data includes every team member from California-based football teams, it would be still considered a sample unless it encompasses every team member ever.
For calculating population mean, standard deviation, and weights (i), one would need the full set of population data to compute these statistics accurately.
As per (Figure 2.48), the shape of a box plot can provide insights into the distribution of data for the car series, including symmetry, distribution, and potential outliers. For comparative purposes, like the travel habits of different nationalities in Figure 2.45, box plots can reveal differences in central tendency and variability between groups.
Lastly, in (Figure A3), the line graph showing length and median weight relationships can help healthcare providers assess children's development, showing a rough track of physical development by comparing the child's measurements to the data presented in the graph.