Percentiles and Quartiles

Finding Percentiles

Notice how you can find the word “percent” in the word percentile. When we are looking at data, percentiles can help us figure out the relative standing of a value WITHIN our sample. How do we find the percentile of a value?

Sort the values from smallest to largest.
Count the number of values in our data. In other words, what is the sample size?
Count the number of values that are less than the value of interest.
DIVIDE step 3 by step 4
Multiply by 100

Example: 10 exam scores, including your own, are collected. You want to know how well you did when compared to your peers. Find the percentile of you score of 72.

Exam Scores: 55, 63, 54, 34, 56, 72, 77, 65, 45, 68

1. Sort the values from smallest to largest.

34, 45, 54, 55, 56, 63, 65, 68, 72, 77

2. Count the number of values in our data. In other words, what is the sample size?

There are 10 exam scores

3. Count the number of values that are less than the value of interest.

There are 8 scores less than your score of 72

4. DIVIDE step 3 by step 4

8 divided by 10 is 0.80

5. Multiply by 100

0.80 times 100 is 80

Good Job! In this sample, your score is at the 80th percentile! This means that 80 percent of scores are lower than yours. SO impressive.

Quartiles

As the “quart” part of the name implies, there are 4 quartiles. Q1 is the 25th percentile. Q2 is the 50th percentile or in other words, the median. Q3 refers to the 75th percentile. Q4 is just the largest number in your data set. How do find values from percentiles?

Sort your data from smallest to largest
Multiply your sample size with your percentile. This gives you the LOCATION of the number you’re looking for. THIS IS NOT THE FINAL ANSWER
There are two possible scenarios for this step
- If your answer is NOT a whole number, round to the next number. This will be the location of your answer if you start counting from the lowest value.
- If your answer IS a whole number, take the value of this this location and ADD it with the next value. Then divide by 2.

Example: Find the value of Q1 and Q2 using the same exam scores from the pervious example.

1. Sort your data from smallest to largest

34, 45, 54, 55, 56, 63, 65, 68, 72, 77

2. Multiply your sample size with your percentile. This gives you the LOCATION of the number you’re looking for. THIS IS NOT THE FINAL ANSWER

Q1 = 25th percentile therefore, multiply 0.25 times the sample size of 10. This equals 2.5

Q2 = 50th percentile therefore, multiply 0.50 times the sample size of 10. This equals 5.0

3. There are two possible scenarios for this step
a. If your answer is NOT a whole number, round to the next number. This will be the location of your answer if you start counting from the lowest value.
2.5 is not a whole number, therefore we round to 3. The third number in our data is 54. This is your answer.

b. If your answer IS a whole number, take the value of this this location and ADD it with the next value. Then divide by 2.
5 is a whole number, therefore we are going to take the 5th and 6th number in our data and add them. 56 + 63 = 119. The we divide this number by 2. 119 divided by 2 is 59.5. This is your answer.