Question

the list shows the mileage rating (in mpg) for some 2019 vehicles with all - wheel or four - wheel drive.
11, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18,
18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21,
21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24,
24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 29,
30, 31, 32, 33, 34
which intervals are most appropriate for a histogram displaying the mileage ratings?
0 - 15, 15 - 30, 30 - 45
0 - 20, 20 - 40, 40 - 60
10 - 15, 15 - 20, 20 - 25, 25 - 30, 30 - 35
0 - 5, 5 - 10, 10 - 15, 15 - 20, 25 - 25, 25 - 30

Explanation:

Step1: Analyze data range

The smallest value is 11 and the largest value is 34.

Step2: Check interval logic

For a histogram, intervals should be non - overlapping and cover the entire data range.

• Option 0 - 5, 5 - 10, 10 - 15, 15 - 20, 25 - 25, 25 - 30: The interval 25 - 25 is not a valid interval (width = 0), and it skips 20 - 25.
• Option 10 - 15, 15 - 20, 20 - 25, 25 - 30, 30 - 35: Covers the range from 11 to 34 (11 is close to 10, 34 is close to 35). Intervals are non - overlapping and of equal width (width = 5).
• Option 0 - 20, 20 - 40, 40 - 60: The width is 20. But most of the data (except a few values like 30, 31, 32, 33, 34) is in the 0 - 20 range. This will make the histogram not well - distributed.
• Option 0 - 15, 15 - 30, 30 - 45: The width of the first two intervals is 15 and the last is 15. But the data in the 15 - 30 interval will be too crowded compared to the 0 - 15 and 30 - 45 intervals.

Answer:

10 - 15, 15 - 20, 20 - 25, 25 - 30, 30 - 35