Questions: Analyze the distribution of faculty numbers across different class boundaries: Number of College Faculty The number of faculty for a variety of private colleges that offer only bachelor's degrees is listed below in a frequency distribution. Class boundaries Frequency 76.5-111.5 3 111.5-146.5 6 146.5-181.5 5 181.5-216.5 4 216.5-251.5 3 251.5-286.5 3 286.5-321.5 2 321.5-356.5 0 356.5-391.5 1 Total 27

Solution Steps

To analyze the distribution of faculty numbers across different class boundaries, we can calculate the relative frequency for each class boundary. The relative frequency is the frequency of a class divided by the total number of observations. This will help us understand the proportion of colleges that fall into each class boundary.

We have a frequency distribution of faculty numbers across different class boundaries. The class boundaries are given as intervals, and the corresponding frequencies are provided for each interval.

The total number of observations is the sum of all frequencies. Given the frequencies $[3, 6, 5, 4, 3, 3, 2, 0, 1]$, the total number of observations is: $$\text{Total Observations} = 3 + 6 + 5 + 4 + 3 + 3 + 2 + 0 + 1 = 27$$

The relative frequency for each class boundary is calculated by dividing the frequency of each class by the total number of observations. The relative frequencies are as follows:

• For class boundary $76.5-111.5$: $\frac{3}{27} \approx 0.1111$
• For class boundary $111.5-146.5$: $\frac{6}{27} \approx 0.2222$
• For class boundary $146.5-181.5$: $\frac{5}{27} \approx 0.1852$
• For class boundary $181.5-216.5$: $\frac{4}{27} \approx 0.1481$
• For class boundary $216.5-251.5$: $\frac{3}{27} \approx 0.1111$
• For class boundary $251.5-286.5$: $\frac{3}{27} \approx 0.1111$
• For class boundary $286.5-321.5$: $\frac{2}{27} \approx 0.0741$
• For class boundary $321.5-356.5$: $\frac{0}{27} = 0.0000$
• For class boundary $356.5-391.5$: $\frac{1}{27} \approx 0.0370$

Final Answer