Percentiles are values that divide a ranked distribution into 100 equal parts. The nth percentile is the value below which n% of the data falls, telling you where a specific observation stands relative to the entire dataset.
Being in the 90th percentile means you scored better than 90% of people. It's not about your raw score - it's about your position relative to everyone else.
Showing a random 20 of 50 problems.
Example 1
medium
On a test, Maria's percentile rank is 92 while Ron's is 80. If 500 students took the test, about how many more students scored below Maria than below Ron?
Example 2
challenge
Two students both score 700. In test A (700 is the 95th percentile) and test B (700 is the 60th percentile), which performance is relatively stronger and why?Test A: a score of 700 falls at the 95th percentile โ above 95% of test-takers (shaded).
Example 3
easy
The first quartile Q1โ corresponds to which percentile?Q1 falls at which percentile?
Example 4
hard
A data set of 1000 values has the 95th percentile equal to 200. Roughly how many values exceed 200?
Example 5
easy
A baby's weight is in the 5th percentile. Should the pediatrician be concerned about being below most peers?
Example 6
challenge
In an ordered data set of n=8 values 3,5,6,8,11,13,17,20, find the 25th percentile using the locator L=10025โร8 and the convention 'if L is a whole number, average positions L and L+1'.Find Q1 (the 25th percentile) for the data set {3, 5, 6, 8, 11, 13, 17, 20}.
Example 7
easy
Being in the 99th percentile for height means you are taller than what percent of people?At the 99th percentile, 99% of the group falls below (shaded).
Example 8
medium
The IQR is built from which two percentiles, and what does it measure?The IQR spans from the 25th percentile (Q1) to the 75th percentile (Q3), covering the middle 50% of the data.
Example 9
medium
For a normal distribution with mean 100 and SD 15, the 50th percentile is what value?
Example 10
medium
Why is a percentile rank often more informative than a raw score on a standardized test?
Example 11
medium
A standardized test gives Carla a score of 1200 at the 78th percentile and Don a score of 1320 at the 88th percentile. Whose score is higher in percentile rank?
Example 12
easy
A student's score is in the 92nd percentile. What percent of test-takers did the student score above (or equal to)?
Example 13
easy
The third quartile Q3โ corresponds to which percentile?Q3 falls at which percentile?
Example 14
hard
In a normally distributed data set with mean 500 and standard deviation 100, approximately what value corresponds to the 84th percentile? (Hint: use the empirical rule โ 84% is one standard deviation above the mean.)
Example 15
easy
Higher percentile rank means a ____ position relative to the group.
Example 16
easy
The 25th percentile is also called the ____ quartile.
Example 17
medium
In the ranked list 2,5,7,8,11,14 (6 values), the value 8 has 3 of 6 values at or below partial-count... using rank below: 3 of 6 values are below 8. Estimate its percentile.
Example 18
medium
Given the sorted data set of 20 values: 12, 15, 18, 20, 22, 25, 27, 30, 32, 35, 38, 40, 42, 45, 48, 50, 55, 60, 65, 70. Find the value at the 40th percentile.
Example 19
hard
A normal distribution with ฮผ=500 and ฯ=100 has the 16th percentile at approximately what value?
Example 20
easy
Does a higher percentile rank mean a higher relative standing in the data?