3. Describing Data Numerically
Describing Data Numerically Using a Graphing Calculator
1:12 minutesProblem 2.R.43
Textbook Question
A student’s test grade of 75 represents the 65th percentile of the grades. What percent of students scored higher than 75?
Verified step by step guidance1
Understand the concept of percentiles: The 65th percentile means that 65% of the students scored less than or equal to the given grade (75 in this case).
Recognize that the remaining percentage of students scored higher than the 65th percentile. To find this, subtract the percentile value (65%) from 100%.
Set up the calculation as: \( 100\% - 65\% \).
Simplify the subtraction to determine the percentage of students who scored higher than 75.
Interpret the result: The final value represents the proportion of students who scored above the grade of 75.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Percentile
A percentile is a statistical measure that indicates the value below which a given percentage of observations fall. For example, if a student's score is at the 65th percentile, it means that 65% of the students scored below that score. Understanding percentiles helps in interpreting how a particular score compares to the rest of the data set.
Cumulative Distribution
A cumulative distribution function (CDF) shows the probability that a random variable takes on a value less than or equal to a specific value. In the context of percentiles, the CDF helps to determine the proportion of scores that fall below a certain threshold, which is essential for understanding how many students scored higher than a given score.
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Complementary Percentage
The complementary percentage refers to the portion of a population that exceeds a certain value. In this case, if 65% of students scored below 75, then 100% - 65% = 35% of students scored higher than 75. This concept is crucial for answering questions about relative performance in a statistical context.
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