Question

discrete random variables – mean
*fv stats b beads: 2023-2024
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.

grade	4	3	2	1	0

what is the median of the distribution?
options: 2.98, 3, 2, 3.50

Explanation:

Step1: Calculate cumulative probabilities

First, we list the grades and their probabilities:

• Grade 4: Probability = 0.4, Cumulative Probability = 0.4
• Grade 3: Probability = 0.32, Cumulative Probability = 0.4 + 0.32 = 0.72
• Grade 2: Probability = 0.17, Cumulative Probability = 0.72 + 0.17 = 0.89
• Grade 1: Probability = 0.08, Cumulative Probability = 0.89 + 0.08 = 0.97
• Grade 0: Probability = 0.03, Cumulative Probability = 0.97 + 0.03 = 1.00

Step2: Find the median

The median is the smallest value \( x \) such that the cumulative probability is at least 0.5.

Looking at the cumulative probabilities:

• For Grade 4, cumulative probability is 0.4 (less than 0.5)
• For Grade 3, cumulative probability is 0.72 (at least 0.5)

So the median is 3.

Answer:

3