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:C
20 scores, with 5 less than 2.34
5 is 25% of 20, so the 25th %ile
or 6 <= 2.34, making it the 30th %ile
To find the percentile of a GPA of 2.34 in the given data set, you can follow these steps:
Step 1: Arrange the data set in ascending order:
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: Count the total number of data points. In this case, there are 20 GPAs.
Step 3: Calculate the rank of the GPA you're interested in. In this case, the rank of 2.34 is 6 because it is the 6th value when the data set is arranged in ascending order.
Step 4: Calculate the percentile using the formula: (rank / total number of data points) * 100.
In this case, the percentile of a GPA of 2.34 would be (6/20) * 100, which is equal to 30.
Therefore, a GPA of 2.34 would be approximately in the 30th percentile.
So, the correct answer is C. About the 30th.