Final answer:
To construct a box plot from the given data, find the minimum value, first quartile, median, third quartile, and maximum value. Then draw a number line and connect the values to create the box plot.
Step-by-step explanation:
To construct a box plot from the given data, you need to first find the five number summary: the minimum value, first quartile (Q₁), median (Q₂), third quartile (Q₃), and the maximum value.
For the given data: 85, 84, 52, 92, 52, 60, 57, 45, 55, 71
The minimum value is 45.
Arrange the data in ascending order: 45, 52, 52, 55, 57, 60, 71, 84, 85, 92.
The first quartile (Q₁) is the median of the lower half of the data, which is 55.
The median is the median of the entire data set, which is 60.
The third quartile (Q₃) is the median of the upper half of the data, which is 84.
The maximum value is 92.
Now, we can construct the box plot using these values on a number line. Draw a horizontal line and mark the minimum and maximum values at the ends. Draw a vertical line at the first quartile (Q₁), median (Q₂), and third quartile (Q₃). Connect the lines from Q₁ to Q₃ to form the box. Finally, draw a line, or whisker, from the box to the minimum and maximum values.