Final answer:
Hank's histogram using intervals of 6-10, 11-15, etc., resulted in 5 bars with the tallest bar at the 16-20 interval having a height of 5. Lisa's histogram with intervals of 0-9, 10-19, etc., also had 5 bars, with the tallest bar at the 10-19 interval having a height of 7. Other ways of displaying the data include bar graphs, frequency tables, pie charts, and box-and-whisker plots.
Step-by-step explanation:
To answer the student's question regarding histograms and class sizes at West middle school:
- For Hank's histogram with intervals of 6-10,11-15, and so on, the number of bars (classes) would be determined by the range of the values and the interval width. In this case, the values range from 7 to 28, so the intervals will be 6-10, 11-15, 16-20, 21-25, 26-30, giving us a total of 5 bars. The height of the highest bar would correspond to the interval with the most number of classes falling within it. After tallying, the interval 16-20 has the most, with 5 classes falling within it.
- For Lisa's histogram using intervals of 0-9, 10-19, and so on, similar reasoning shows we also have 5 bars since the intervals will be 0-9, 10-19, 20-29, 30-39 and 40-49 (even though we have no values reaching that high). The interval with the highest frequency is 10-19, containing 7 classes, so the height of the highest bar is 7.
- Besides a histogram, other ways to display these data include a bar graph, a frequency table, a pie chart (for relative frequencies), or a box-and-whisker plot to show the distribution of data.