Final answer:
The scores that separate the middle 28th percentile are determined by finding the value below which 28 percent of the scores fall in an ordered list, while the 70th percentile score is the value below which 70 percent fall. The first and third quartiles represent the middle 50 percent of the scores.
Step-by-step explanation:
The scores that separate the middle 28th percentile are found using cumulative frequency and understanding percentile positions. Finding specific percentiles such as the 28th and 70th involves locating the position of scores in an ordered list that corresponds to the given percentage.
For example, the 70th percentile score is the value below which 70 percent of the scores fall. Given an ordered list, this can be found by counting the scores up to that point. If there are 50 scores, to find the 70th percentile, you would locate the 35th score (since 70% of 50 is 35). If the data set has an even number of observations, like 14, to find the median (which is the 50th percentile), you would average the 7th and 8th scores.
To find the first and third quartiles, which represent the middle 50 percent of the scores, the data set is split into quarters. The first quartile (Q1) is the middle score of the lower half of the data set, and the third quartile (Q3) is the middle score of the upper half. Therefore, the middle 50 percent of the exam scores lie between the first and third quartiles.