The following data set is the GPAs of the students in a statistics class.
1.93, 1.99, 2.00, 2.04, 2.12, 2.34, 2.55, 2.55, 2.75, 2.75,
2.80, 2.80, 2.85, 3.02, 3.12, 3.22, 3.31, 3.33, 3.45, 3.69
What percentile is a GPA of 2.34?
A. About the 6th
B. About the 15th
C. About the 30th
D. About the 60th
Answer A
Assuminga normal distribution, find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
I'll let you do the calculations.
thanks
Welcome
To find the percentile of a given GPA in the dataset, we can use the following steps:
Step 1: Sort the dataset in ascending order.
The sorted dataset:
1.93, 1.99, 2.00, 2.04, 2.12, 2.34, 2.55, 2.55, 2.75, 2.75,
2.80, 2.80, 2.85, 3.02, 3.12, 3.22, 3.31, 3.33, 3.45, 3.69
Step 2: Determine the rank of the given GPA.
The rank is the position of the GPA in the sorted dataset. In this case, the GPA 2.34 is located in the 6th position.
Step 3: Calculate the percentile.
The percentile can be calculated using the formula:
Percentile = (Rank / Total number of data points) * 100
In this case, the total number of data points is 20. So, applying the formula:
Percentile = (6 / 20) * 100 = 30%
Therefore, a GPA of 2.34 is at about the 30th percentile.
So, the correct answer is C. About the 30th.