Questions: A state trooper collected and recorded speeds of several cars at a set location on a local highway. The speeds in miles per hour are recorded below. Which of the following is the median of this data set? 73,81,68,75,90,78,75,82,77,71

Solution Steps

The speeds of the cars recorded are: \[ 73, 81, 68, 75, 90, 78, 75, 82, 77, 71 \]

First, we sort the data in ascending order: \[ \text{Sorted data} = [68, 71, 73, 75, 75, 77, 78, 81, 82, 90] \]

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 \( N \) is the number of data points.

Since the rank is \( 5.5 \), we need to average the values at ranks \( 5 \) and \( 6 \): \[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{75 + 77}{2} = 76.0 \]

Final Answer