Question

question 6 of 9
stacked
the histograms applet displays the travel times to campus in minutes on a particular tuesday for a sample of 20 students.
now set the applet to 6 classes.
in which class do most of the data values lie?
lower bound of the class:
upper bound of the class:
how many students have travel times in this class?
number of students:

Explanation:

Step1: Identify the tallest bar

The histogram has bars with counts. The tallest bar (highest count) is the one with the maximum height. From the graph, the tallest bar is between 10 and 20? Wait, no, looking at the x - axis labels (0,10,20,30,40) and the bar heights. Wait, the first bar (after 0) is around 5 - 10? No, let's check the x - axis intervals. The total range is from 0 to 40, with 6 classes. So the class width is \( \frac{40 - 0}{6}\approx6.67 \), but maybe the classes are 0 - 10, 10 - 20, 20 - 30, 30 - 40? No, the graph shows bars at positions. Wait, the tallest bar has a count of 7. Let's see the x - axis: the first bar starts at 5? No, the leftmost bar (after 0) has a lower bound? Wait, the x - axis has marks at 0,10,20,30,40. The tallest bar is between 10 and 20? Wait, no, looking at the bar heights: the bar with the highest height (count = 7) is between 10 and 20? Wait, no, the x - axis labels: the first bar (from 5 to 15? No, maybe the classes are 0 - 10, 10 - 20, 20 - 30, 30 - 40, but with 6 classes. Wait, the problem says set to 6 classes. So the range is 0 to 40, so class width is \( \frac{40}{6}\approx6.67 \), so classes are 0 - 6.67, 6.67 - 13.33, 13.33 - 20, 20 - 26.67, 26.67 - 33.33, 33.33 - 40. But from the graph, the tallest bar is the one with the highest count. Looking at the y - axis (count), the tallest bar has count 7. Let's check the x - axis: the bar with count 7 is between 10 and 20? Wait, no, the x - axis marks are at 0,10,20,30,40. The bar with the highest height is between 10 and 20? Wait, no, the first bar (after 0) has a count of 3, then 2, then 7, then 4, then 2, then 2? Wait, no, the y - axis is count (0 - 10). The tallest bar is the third bar (if we start from 0). Wait, the x - axis labels: 0,10,20,30,40. So the classes are 0 - 10, 10 - 20, 20 - 30, 30 - 40? No, with 6 classes, the class width is \( \frac{40}{6}\approx6.67 \), so classes: 0 - 6.67, 6.67 - 13.33, 13.33 - 20, 20 - 26.67, 26.67 - 33.33, 33.33 - 40. But from the graph, the tallest bar is between 10 and 20? Wait, the bar with count 7 is between 10 and 20? Wait, the x - axis has a mark at 10, 20, etc. So the lower bound of the class with the most data: looking at the graph, the tallest bar (highest count) is between 10 and 20? Wait, no, the first bar (from 5 to 15) has count 3, then 10 - 15? No, maybe the classes are 0 - 10, 10 - 20, 20 - 30, 30 - 40, but with 6 classes, so maybe 0 - 6.67, 6.67 - 13.33, 13.33 - 20, 20 - 26.67, 26.67 - 33.33, 33.33 - 40. But the tallest bar (count = 7) is in the class 10 - 20? Wait, no, the x - axis mark at 10: the bar to the right of 10 (between 10 and 20) has the highest count. Wait, the lower bound: let's see, the tallest bar's lower bound. From the graph, the tallest bar is between 10 and 20? Wait, the x - axis labels: 0,10,20,30,40. The bar with the highest height (count 7) is between 10 and 20? Wait, no, the first bar (after 0) is from 0 - 10? No, the first bar (leftmost) has a count of 3, then 2, then 7, then 4, then 2, then 2. So the class with the most data (highest count) is the one with count 7. Now, the x - axis: the class with count 7 is between 10 and 20? Wait, the x - axis marks are at 0,10,20,30,40. So the class with the tallest bar (count 7) has a lower bound of 10? Wait, no, maybe the classes are 0 - 10, 10 - 20, 20 - 30, 30 - 40, but with 6 classes, so maybe 0 - 6.67, 6.67 - 13.33, 13.33 - 20, 20 - 26.67, 26.67 - 33.33, 33.33 - 40. But from the graph, the tallest bar is between 10 and 20 (since the bar is centered around 15? No, the key is that the tallest bar (highest count) is in the class with lower bound 10 and upper bound 20? Wait, no, looking at the x - axis, the bar with count 7 is between 10 and 20. So lower bound of the class: 10, upper bound: 20? Wait, no, maybe the class is 10 - 20. Then the number of students (count) is 7.

Step2: Determine the class bounds and count

- The tallest bar (highest count) has a count of 7.
- The lower bound of the class: Looking at the x - axis, the class with the tallest bar is between 10 and 20 (since the x - axis marks are at 10,20, etc., and the bar is between 10 and 20).
- The upper bound is 20 (or 20, since the next bar starts at 20).
- The number of students (count) is 7.

Wait, maybe the classes are 0 - 10, 10 - 20, 20 - 30, 30 - 40, but with 6 classes, so maybe the width is 6.67, but the graph shows the tallest bar at 10 - 20 (with count 7). So:

Lower bound of the class: 10 (assuming the class is 10 - 20)
Upper bound of the class: 20
Number of students: 7

Answer:

lower bound of the class: \( \boldsymbol{10} \)
upper bound of the class: \( \boldsymbol{20} \)
Number of students: \( \boldsymbol{7} \)