A group of friends tracked the number of hours they watched TV in a week. The data set is given. \[ \{8,6,9,6,8,9,8,6,6,8,9,8,9\} \] Find and interpret the mean and median number of hours of TV watching. Round numbers to the nearest tenth if necessary. Mean \( = \) \( \square \) Median = \( \square \) The values of the mean and median tell us that the data set Write an optional reasoning for your answer: shows a fairly normal distribution is slightly skewed or contains an outlier

\[ \textbf{Step 1: Compute the Mean} \] We have 13 observations: \[ \{8,6,9,6,8,9,8,6,6,8,9,8,9\} \] Count the frequency: - \(6\) appears 4 times - \(8\) appears 5 times - \(9\) appears 4 times Now, compute the sum: \[ \text{Sum} = 4(6) + 5(8) + 4(9) = 24 + 40 + 36 = 100 \] The mean is: \[ \text{Mean} = \frac{100}{13} \approx 7.7 \] \[ \textbf{Step 2: Find the Median} \] First, sort the data: \[ \{6,6,6,6,8,8,8,8,8,9,9,9,9\} \] For 13 values, the median is the \(\frac{13+1}{2} = 7^\text{th}\) number in the ordered list. Counting to the 7th element: \[ \underbrace{6,6,6,6}_{\text{first 4}},\underbrace{8,8,8}_{\text{5th, 6th, 7th}}, \dots \] Thus, the median is: \[ \text{Median} = 8 \] \[ \textbf{Step 3: Interpretation} \] The mean is approximately \(7.7\) hours and the median is \(8\) hours. The fact that the mean is very close to the median indicates that the data is fairly balanced. There is no significant skew or extreme outlier affecting the average. \[ \textbf{Final Answers:} \] \[ \text{Mean} = 7.7 \quad \text{hours}, \quad \text{Median} = 8 \quad \text{hours.} \] \[ \textbf{Interpretation:} \text{The values of the mean and median tell us that the data set shows a fairly normal distribution.} \]