Question

the final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with ( a = 4 ), ( b = 3 ), ( c = 2 ), ( d = 1 ), and ( f = 0 ). let ( x ) represent the grade for a randomly selected student from the class.
what is the median of the distribution?
2
3
2.98
3.00

Explanation:

Step1: Calculate cumulative probabilities

Cumulative probability for grade \(4\): \(P(X = 4)=0.4\)
Cumulative probability for grade \(3\): \(P(X = 4)+P(X = 3)=0.4 + 0.32=0.72\)
Cumulative probability for grade \(2\): \(0.4+0.32 + 0.17=0.89\)
Cumulative probability for grade \(1\): \(0.4+0.32+0.17 + 0.08=0.97\)
Cumulative probability for grade \(0\): \(0.4+0.32+0.17+0.08 + 0.03 = 1\)

Step2: Determine the median

The median \(m\) is the value such that \(P(X\leq m)\geq0.5\) and \(P(X\geq m)\geq0.5\)
Since \(P(X = 4)=0.4<0.5\) and \(P(X = 4)+P(X = 3)=0.72\geq0.5\)

Answer:

\(3\)