Given the data set: \[ 6, 8, 10, 12, 13, x \quad \text{(where } n = 6 \text{)} \] Mean of the data: \[ = \cfrac{6 + 8 + 10 + 12 + 13 + x}{6} = \cfrac{49 + x}{6} \] Since \(n = 6\), the median is the average of the 3rd and 4th terms: \[ = \cfrac{10 + 12}{2} = 11 \] According to the question, mean = median = 11 \[ \Rightarrow \cfrac{49 + x}{6} = 11 \Rightarrow 49 + x = 66 \Rightarrow x = 66 - 49 = 17 \] Therefore, the value of \(x\) is 17.