To find the sample mean for student applications, let's follow these steps:
1. List the data points: The number of student applications for each semester are given as follows:
[tex]\[
106, 137, 285, 120, 202, 195, 327, 139, 307, 318, 212, 217
\][/tex]
2. Sum the data points: Add all the individual values.
[tex]\[
106 + 137 + 285 + 120 + 202 + 195 + 327 + 139 + 307 + 318 + 212 + 217 = 2,565
\][/tex]
3. Count the number of data points: There are 12 data points in the list.
4. Calculate the sample mean: The sample mean is the total sum of the data points divided by the number of data points.
[tex]\[
\text{Sample Mean} = \frac{\text{Total Sum of Data Points}}{\text{Number of Data Points}} = \frac{2,565}{12} \approx 213.75
\][/tex]
Given the options:
- A. 2,565 (which is the total sum, not the mean)
- B. 32.9 (which is incorrect)
- C. 256.5 (which is incorrect)
- D. 214
The closest and most appropriate answer is:
[tex]\[
\boxed{214}
\][/tex]
