Questions: The following list contains the number of hours that a sample of 10 middle-school students spent watching television last week. 8, 14, 11, 19, 19, 11, 20, 15, 10, 12 Find the median number of hours for that sample.

Solution Steps

The first step is to sort the given data set of hours spent watching television by the students. The sorted data is:

\[ [8, 10, 11, 11, 12, 14, 15, 19, 19, 20] \]

To find the median, we use the formula for the rank:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (10 + 1) = 5.5 \]

where \( Q \) is the quantile (0.5 for the median) and \( N \) is the number of data points (10).

Since the rank is 5.5, we need to average the values at the 5th and 6th positions in the sorted data:

\[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{12 + 14}{2} = 13.0 \]

Final Answer