Question

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let X represent the score on a randomly selected exam. The distribution of scores for one subject’s standardized test is given in the table.

A 2-column table with 5 rows. Column 1 is labeled score with entries 1, 2, 3, 4, 5. Column 2 is labeled probability with entries 0.18, 0.20, 0.26, 0.21, 0.15.

What is the median of the distribution?

2.5
2.95
3
3.5

Answer 1

To determine the median of the distribution, we need to find the score that divides the distribution into two equal halves.

First, we need to calculate the cumulative probability for each score. The cumulative probability is the sum of the probabilities from the first score up to that score.

For score 1, the cumulative probability is 0.18.
For score 2, the cumulative probability is 0.18 + 0.20 = 0.38.
For score 3, the cumulative probability is 0.38 + 0.26 = 0.64.
For score 4, the cumulative probability is 0.64 + 0.21 = 0.85.
For score 5, the cumulative probability is 0.85 + 0.15 = 1.00.

The median is the score where the cumulative probability is 0.5. Looking at the cumulative probabilities, we can see that the score that represents a cumulative probability of 0.5 is between score 3 and score 4.

Therefore, the median of the distribution is 3.5.