Your medical terminology instructor listed the following grades for the class out of a 75 – point test: 33, 34, 43, 45, 45, 54, 55, 59, 60, 62, 64, 66, 67, 68, 67, 68, 68, 69, 70, 70.
find the 90th percentile
There are 20 grades, so the top 2 scores form the 90th %ile.
To find the 90th percentile of a given dataset, you need to first arrange the data in ascending order. Then, determine the position of the percentile using the formula:
Position = (p/100) * (n + 1)
where p is the desired percentile (90 in this case) and n is the total number of data points.
Let's calculate the 90th percentile for the grades in the class:
First, sort 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
Next, calculate the position using the formula:
Position = (90/100) * (20 + 1) = 0.9 * 21 = 18.9
Since the position is not a whole number, we need to consider the value at the 18th position and the value at the 19th position.
The 18th value is 69, and the 19th value is 70.
To find the 90th percentile, we interpolate between these two values. Interpolation is done by taking the average of the two values.
90th Percentile = (69 + 70) / 2 = 139 / 2 = 69.5
Therefore, the 90th percentile for the given grades is 69.5.