Example of a Percentile Rank

By definition, what does the percentile rank of an individual score indicate within a distribution?

If a participant in a research study has a percentile rank of 80 on a standardized test, it means that 80% of the scores in the distribution are higher than that participant's score.

A researcher is evaluating scores from a group of 40 participants on a standardized memory test. Based on the number of participants who scored strictly lower than a specific individual, match each result to its corresponding percentile rank.

A school psychologist is evaluating test results from a diagnostic literacy assessment to determine the priority for academic intervention. The goal is to provide support to students with the lowest relative standing in their respective distributions first. Order the following students from highest priority for support (the lowest relative standing) to lowest priority for support (the highest relative standing) based on their percentile rank data.

Example of Calculating Percentile Ranks

In a developmental psychology study, two children of different ages take the same memory assessment. A researcher reports that both children are at the $75^{th}$ percentile for their respective age-group distributions. What does this information communicate about their performance?

In a psychological study involving a sample of $N = 60$ participants, a researcher finds that a specific raw score has a percentile rank of $80$. If the researcher excludes $10$ participants who all achieved scores strictly lower than this raw score, the new percentile rank for that same score would be _____. (Provide the numeric value only, rounded to the nearest whole number.)

The _____ of a specific score describes its relative location within a distribution and is defined as the percentage of all scores in the distribution that are strictly lower than that score.

A researcher administers a standardized cognitive test to a sample of $N = 50$ participants. Participant A scores $85$ points on the test. If exactly $40$ participants in the sample scored strictly lower than $85$, then the percentile rank of Participant A's score is $80$.

A psychologist analyzes the achievement test scores of a sample of $N = 200$ students. Match each participant's test performance outcome to their corresponding percentile rank based on the number of scores that are strictly lower than theirs.

A developmental psychologist evaluates the relative reading ability of four children using their scores on a standardized literacy assessment. Order the children from the lowest relative standing (lowest percentile rank) to the highest relative standing (highest percentile rank) to prioritize academic intervention.

In a concise analytical response, define the concept of a percentile rank and describe its primary purpose when analyzing quantitative data from a sample.

Based on the definition of percentile rank, justify why the participant's interpretation is incorrect and explain what the $85^{th}$ percentile rank actually represents regarding their performance.

If a psychologist finds that exactly half of the scores in a participant distribution are strictly lower than a specific individual's score, what is that individual's percentile rank? Provide a brief one-sentence justification based on the definition of the term.