Question

Divide the range of data into five equally spaced intervals. What are the intervals?

a) 0-20, 21-40, 41-60, 61-80, 81-100
b) 0-10, 11-30, 31-50, 51-70, 71-90
c) 0-25, 26-50, 51-75, 76-100, 101-125
d) 0-5, 6-15, 16-25, 26-35, 36-45

Answer 1

To create five equally spaced intervals, calculate the interval width by dividing the total range by five, then sequentially add this width to the starting point to establish the intervals.

Step-by-step explanation:

To divide the range of data into five equally spaced intervals, we need to calculate the interval width first using the provided range. For example, using the reference information c., the data range is from 32.5 to 100.5, so the width of one interval is (100.5 - 32.5) / 5, which equals 13.6. Hence, the intervals would be 32.5-46.1, 46.1-59.7, 59.7-73.3, 73.3-86.9, and 86.9-100.5. Each interval includes the lower endpoint but not the upper endpoint, ensuring that no data value falls on an interval boundary.

The process consists of the following calculation steps for determining intervals:

1. Subtract the smallest value of the range from the largest value to find the total range.
2. Divide the total range by the number of desired intervals to get the interval width.
3. Create each interval by adding the interval width to the starting point until the end of the range is reached.