Let's solve the problem step-by-step:
1. Identify the range of the data set:
The data set ranges from 2 inches to 38 inches.
2. Determine the number of intervals:
There are 13 lines on the axis of the graph. This means there are 12 intervals (since [tex]\(13 - 1 = 12\)[/tex]) between these lines.
3. Calculate the data interval length:
To find the length of each interval, subtract the minimum value from the maximum value of the data set and divide by the number of intervals.
[tex]\[
\text{Interval} = \frac{(\text{data\_max} - \text{data\_min})}{(\text{num\_lines} - 1)}
\][/tex]
Substituting the given values:
[tex]\[
\text{Interval} = \frac{(38 - 2)}{(13 - 1)} = \frac{36}{12} = 3.0
\][/tex]
4. Round up to the nearest whole or half number:
The calculated interval length is 3.0. Since 3.0 is already a whole number, there is no need to round up further.
Therefore, the lines on the graph should be labeled:
Every 3 inches.
