You are one of the finalists at a science fair. The scores of the other finalists are 87, 89, 81, 85, 87, 83, 86, 94, 90, 97, 80, 89, 85, and 88. Write an inequality that represents your possible scores if your percentile rank is 80.
To write an inequality that represents your possible scores, we need to determine the range of scores that correspond to the 80th percentile rank.
To do this, we first need to find the position of the 80th percentile within the dataset. The percentile rank is determined by finding the percentage of values that are less than or equal to a given score. In other words, if you are at the 80th percentile, 80% of the scores in the dataset should be less than or equal to your score.
To find the position of the 80th percentile, we need to determine how many scores are below you in the dataset. There are a total of 14 scores (including yours) in the dataset, so we can calculate the position as follows:
Position = 80% * 14
Position = 0.8 * 14
Position = 11.2
Since the position is not a whole number, we will round it up to the nearest whole number. This means that 80% of the scores should be less than or equal to the score in the 12th position.
Next, we need to find the score in the 12th position. We can do this by sorting the scores in ascending order:
80, 81, 83, 85, 85, 86, 87, 87, 88, 89, 89, 90, 94, 97
The score in the 12th position is 89.
Since we want to find the range of possible scores that correspond to the 80th percentile, we can write the inequality as follows:
Score ≤ 89
This means that any score that is less than or equal to 89 would be within the range of scores that correspond to the 80th percentile rank.