how to find percentile of frequency distribution curve
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. Percentiles and Percentile Ranks
Percentile Rank - the percentage of individuals in the distribution with scores at or below the particular value.
Percentile - the particular score (X) associated with a percentile rank.
E.g., You scored X=4 on the test (see the distribution below). You know thatroughly 85% of the class had scores of 4 or lower.
Your score has a percentile rank of ____.
Your score of ____ would be called the 85th percentile.
Cumulative frequencies (cf) show the number of individuals located at or below each score
To find percentiles, we must convert these frequencies into percentages.
- The percentages that result are called cumulative percentages (c%)--show the percentage of individuals accumulated as you move up the scale
X f p % cf c%
5 3 .15 15% 20 100%
4 4 .20 20% 17 85%
3 8 .40 40% 13 65%
2 3 .15 15% 5 25%
1 2 .10 10% 2 10%
Now consider example 2.5 on p. 53
Remember that the X values in the table are not points on a scale, but intervals
Each cumulative percentage value is associated with the upper real limit of its interval

Figure 2-13 (p. 53)
The relationship between cumulative frequencies (cf values) and upper real limits. Notice that two people have scores of X= 1. These two individuals are located between the real limits of 0.5 and 1.5. Although their exact locations are not known, you can be certain that both had scores below the upper real limit of 1.5.
Percentile Rank - the percentage of individuals in the distribution with scores at or below the particular value.
Percentile - the particular score (X) associated with a percentile rank.
E.g., You scored X=4 on the test (see the distribution below). You know thatroughly 85% of the class had scores of 4 or lower.
Your score has a percentile rank of ____.
Your score of ____ would be called the 85th percentile.
Cumulative frequencies (cf) show the number of individuals located at or below each score
To find percentiles, we must convert these frequencies into percentages.
- The percentages that result are called cumulative percentages (c%)--show the percentage of individuals accumulated as you move up the scale
X f p % cf c%
5 3 .15 15% 20 100%
4 4 .20 20% 17 85%
3 8 .40 40% 13 65%
2 3 .15 15% 5 25%
1 2 .10 10% 2 10%
Now consider example 2.5 on p. 53
Remember that the X values in the table are not points on a scale, but intervals
Each cumulative percentage value is associated with the upper real limit of its interval

Figure 2-13 (p. 53)
The relationship between cumulative frequencies (cf values) and upper real limits. Notice that two people have scores of X= 1. These two individuals are located between the real limits of 0.5 and 1.5. Although their exact locations are not known, you can be certain that both had scores below the upper real limit of 1.5.
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