Questions: The number of credits being taken by a sample of 13 full-time college students are listed below. Find the mean, median, and mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. 8 10 11 12 8 7 7 7 9 7 7 7 8 Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean is . (Type an integer or decimal rounded to one decimal place as needed.) B. The data set does not have a mean.

Solution Steps

To find the mean of the data set, we use the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( N \) is the number of observations and \( x_i \) are the individual data points. For our data set:

\[ \text{Data} = [8, 10, 11, 11, 8, 7, 7, 9, 7, 7, 9, 7, 8] \]

Calculating the sum of the data:

\[ \sum_{i=1}^{13} x_i = 8 + 10 + 11 + 11 + 8 + 7 + 7 + 9 + 7 + 7 + 9 + 7 + 8 = 109 \]

Now, substituting into the mean formula:

\[ \mu = \frac{109}{13} = 8.4 \]

To find the median, we first sort the data:

\[ \text{Sorted Data} = [7, 7, 7, 7, 8, 8, 9, 9, 10, 11, 11] \]

Since there are 13 observations (an odd number), the median is the middle value, which is the 7th value in the sorted list:

\[ \text{Median} = 9 \]

The mode is the value that appears most frequently in the data set. In our data:

\[ \text{Frequencies: } 7 \text{ appears } 4 \text{ times, } 8 \text{ appears } 3 \text{ times, } 9 \text{ appears } 2 \text{ times, } 10 \text{ appears } 1 \text{ time, } 11 \text{ appears } 2 \text{ times.} \]

Thus, the mode is:

\[ \text{Mode} = 7 \]

Final Answer