How to calculate percentile in educational statistics?
Answers
Answer:
Step-by-step explanation:
Sample question: Find out where the 25th percentile is in the above list.
Step 1: Calculate what rank is at the 25th percentile. Use the following formula:
Rank = Percentile / 100 * (number of items + 1)
Rank = 25 / 100 * (8 + 1) = 0.25 * 9 = 2.25.
A rank of 2.25 is at the 25th percentile. However, there isn’t a rank of 2.25 (ever heard of a high school rank of 2.25? I haven’t!), so you must either round up, or round down. As 2.25 is closer to 2 than 3, I’m going to round down to a rank of 2.
Step 2: Choose either definition 1 or 2:
Definition 1: The lowest score that is greater than 25% of the scores. That equals a score of 43 on this list (a rank of 3).
Definition 2: The smallest score that is greater than or equal to 25% of the scores. That equals a score of 33 on this list (a rank of 2).
Depending on which definition you use, the 25th percentile could be reported at 33 or 43! A third definition attempts to correct this possible misinterpretation:
Definition 3: A weighted mean of the percentiles from the first two definitions.
In the above example, here’s how the percentile would be worked out using the weighted mean:
Multiply the difference between the scores by 0.25 (the fraction of the rank we calculated above). The scores were 43 and 33, giving us a difference of 10:
(0.25)(43 – 33) = 2.5
Add the result to the lower score. 2.5 + 33 = 35.5
In this case, the 25th percentile score is 35.5, which makes more sense as it’s in the middle of 43 and 33.
In most cases, the percentile is usually definition #1. However, it would be wise to double check that any statistics about percentiles are created using that first definition.
Answer:
- Order all the values in the data set from smallest to largest.
- Multiply k percent by the total number of values, n. ...
- If the index obtained in Step 2 is not a whole number, round it up to the nearest whole number and go to Step 4a.