The mean of some observations is 54. If each observation is increased by 8 and its sum is divided by 2, then what is the mean of the resulting observations?
Show Hint
Mean is a linear operator. If you do \(y_i = mx_i + c\), then the new mean is \(\bar{y} = m\bar{x} + c\). Here, \(y_i = \frac{1}{2}(x_i + 8)\), so \(\bar{y} = \frac{1}{2}(54 + 8) = 31\).