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You probably heard of percentiles, or percentile rank, before. Percentile is the same as a relative cumulative frequency, or the percent of data points in, or below, some other bin of data.
IN CONTEXT
You may have seen percentiles reporting standardized test scores. If you were in the 95th percentile on a standardized test, it doesn't mean you scored a 95 on the test. It means that your score was at least as good as 95% of test takers.
Often, large data sets are given in frequency tables, frequently with rounded values.
EXAMPLE
Here is a table showing heights (in inches) of 333 sixth-grade students, along with the frequency, relative frequency, and relative cumulative frequencies.Height | Frequency | Relative Freq | Rel. Cum. Freq | |
---|---|---|---|---|
55 | 11 | 3% | 3% | |
56 | 23 | 7% | 10% | |
57 | 33 | 10% | 20% | |
58 | 36 | 11% | 31% | |
59 | 54 | 16% | 47% | |
60 | 51 | 15% | 62% | |
61 | 43 | 13% | 75% | |
62 | 32 | 10% | 85% | |
63 | 30 | 9% | 94% | |
64 | 13 | 4% | 98% | |
65 | 7 | 2% | 100% |
Question | Answer |
---|---|
Which percentile will a student with a height of 62 inches fall into? | From the chart, you can see that 62 inches falls in the 85th percentile. That means that a 62-inch student is at least as tall as 85% of his/her classmates. |
How tall is a student in the 94th percentile? | They would be 63 inches tall. |
What is the median height for sixth graders? |
This question is a little tricky. By the time you finish counting up through all of the 59-inch students, you still haven't accounted for half the grade yet; only 47% of the students. However, by the time you're done counting all the 60-inch students, you've accounted for 62% of the grade. That means that somewhere within that 60-inch range is the median height. So this tells us that half the students are at or above 60 inches, and half the students are at or below 60 inches. |
EXAMPLE
The following are the measurements (in inches) for the 12 fish caught at the annual Fishing Expo at Cam's local pond:Source: THIS TUTORIAL WAS AUTHORED BY JONATHAN OSTERS FOR SOPHIA LEARNING. PLEASE SEE OUR TERMS OF USE.