Practice Percentiles in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
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.
Example 1
easyA student scored in the 85th percentile on a standardised test with 200 test-takers. What does this mean and how many students scored lower?
Example 2
mediumGiven 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 3
mediumIn a class of 40 students, a student scored higher than 32 others. What percentile is the student at?
Example 4
mediumA baby's weight is at the 25th percentile for her age group. Her parents are worried she is underweight. Is their concern justified? Explain what the 25th percentile means in this context.
Example 5
hardIn 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 — 84% is one standard deviation above the mean.)