your medical terminology instructor listed the following grades for the class out of a 75 point test:<br />
33,34,43,45,45,54,55,59,60,62,64,66,67,68,67,68,68,69,70,70<br />
a.find the 90th percentile<br />
b. your score was 59, what is your percentile?<br />
a. 69
b. 40th percentile
To find the 90th percentile, you need to arrange the grades in ascending order:
33, 34, 43, 45, 45, 54, 55, 59, 60, 62, 64, 66, 67, 68, 67, 68, 68, 69, 70, 70
a. To find the 90th percentile, you can use the following formula:
Position = (Percentile/100) * (N + 1)
where N is the total number of values.
In this case, N = 20.
Position = (90/100) * (20 + 1) = 0.9 * 21 = 18.9
Since the position is not a whole number, we need to round it up to the nearest whole number.
Therefore, the 90th percentile is at position 19.
The 19th value in the list is 68.
So, the 90th percentile is 68.
b. To find your percentile, you can use the following formula:
Percentile = (Position/N) * 100
where N is the total number of values.
In this case, N = 20.
Position = how many scores are less than or equal to your score + 0.5 * how many scores are equal to your score.
The number of scores less than or equal to 59 is 8.
The number of scores equal to 59 is 1.
Position = 8 + 0.5 * 1 = 8.5
Percentile = (8.5/20) * 100 = 42.5
Therefore, your percentile score is 42.5.
To find the 90th percentile, you need to arrange the grades in ascending order and then determine the score that is greater than or equal to 90% of the scores.
Here are the given grades arranged in ascending order:
33, 34, 43, 45, 45, 54, 55, 59, 60, 62, 64, 66, 67, 68, 67, 68, 68, 69, 70, 70
a. To find the 90th percentile, you need to determine the score that is greater than or equal to 90% of the scores. Since there are 20 scores, 90% of 20 scores is 18 (90% x 20 = 18).
The 18th score in the list is 69. Therefore, the 90th percentile score is 69.
b. To find your percentile, you need to determine the percentage of scores that are less than or equal to your score.
Count the number of scores that are less than or equal to 59. In this case, there are 8 scores that are less than or equal to 59.
To calculate the percentile, divide the number of scores less than or equal to your score (8) by the total number of scores (20), then multiply by 100.
(8/20) x 100 = 40
Therefore, if your score is 59, your percentile is 40.