Questions: Professor Ivy records the following scores on her final: 35, 48, 48, 52, 69, 72, 81, 88, 92. What is the median score for the final?

Solution Steps

The given scores are: \[ 35, 48, 48, 52, 69, 72, 81, 88, 92 \] After sorting, the data remains the same: \[ \text{Sorted data} = [35, 48, 48, 52, 69, 72, 81, 88, 92] \]

To find the median, we use the formula for the rank: \[ \text{Rank} = Q \times (N + 1) \] where \( Q = 0.5 \) (for the median) and \( N = 9 \) (the number of scores). Thus, \[ \text{Rank} = 0.5 \times (9 + 1) = 0.5 \times 10 = 5.0 \]

The rank of \( 5.0 \) indicates that the median is the value at position \( 5 \) in the sorted list. The value at this position is: \[ \text{Median} = 69 \]

Final Answer