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Chapter 3: Problem 4

Clayton and Timothy took different sections of Introduction to Economics. Each section had a different final exam. Timothy scored 83 out of 100 and had a percentile rank in his class of 72 . Clayton scored 85 out of 100 but his percentile rank in his class was 70 . Who performed better with respect to the rest of the students in the class, Clayton or Timothy? Explain your answer.

Short Answer

Expert verified
Timothy performed better with respect to his class, as his percentile rank is higher.

Step by step solution

01

Understanding Percentile Rank

The percentile rank tells us the percentage of students who scored less than a particular individual in an exam. A higher percentile rank indicates that a student performed better relative to their peers.
02

Analyzing Timothy's Performance

Timothy scored 83 out of 100, and his percentile rank is 72. This means that Timothy performed better than 72% of his classmates on his exam.
03

Analyzing Clayton's Performance

Clayton scored 85 out of 100, but his percentile rank is 70. This implies that Clayton performed better than 70% of his classmates in his section.
04

Comparing Percentile Ranks

Compare the percentile ranks of Timothy and Clayton. Timothy has a percentile rank of 72, and Clayton has a percentile rank of 70. This means that Timothy performed better than more of his classmates compared to Clayton with respect to their respective class sections.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Percentile Rank
In statistics, a percentile rank describes the percentage of scores that fall below a particular score in a data set. For instance, if a student has a percentile rank of 72, it means the student scored better than 72% of their peers. This measure is particularly useful because it allows us to compare performances across different tests or classes, even when the tests themselves are different. The calculation of percentile rank is crucial in educational settings to gauge how well a student is performing compared to others. It's important to remember that the percentile rank does not directly correlate with the score itself, as it is more about relative performance to the group.
Performance Comparison
When comparing the performances of students such as Clayton and Timothy, one must look beyond the raw scores. Although Clayton scored higher than Timothy in the number of points, his percentile rank is lower. This indicates that fewer classmates scored below him compared to Timothy's class.
  • Timothy: 83/100 with a percentile rank of 72
  • Clayton: 85/100 with a percentile rank of 70
Despite Clayton's higher score, Timothy's higher percentile rank means he performed better in relation to his peers. Understanding this concept is crucial in educational assessments as it points out that absolute scores aren't always indicative of a student's relative standing in class.
The Role of Educational Assessment
Educational assessment involves evaluating a student's performance to provide insights into how they are doing in their learning journey. It plays a vital role not just in individual student evaluation but also in understanding broader educational outcomes. Percentile ranks are a key component of educational assessments as they present a clear picture of where a student stands in relation to their peers.
They highlight both achievements and areas where improvement is needed, helping educators tailor instruction to student needs. Recognizing the distinction between absolute scores and percentile ranks ensures a fair and comprehensive evaluation of academic performance.

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Most popular questions from this chapter

One standard for admission to Redfield College is that the student rank in the upper quartile of his or her graduating high school class. What is the minimal percentile rank of a successful applicant?

What symbol is used for the standard deviation when it is a sample statistic? What symbol is used for the standard deviation when it is a population parameter?

For mallard ducks and Canada geese, what percentage of nests are successful (at least one offspring survives)? Studies in Montana, Illinois, Wyoming, Utah, and California gave the following percentages of successful nests (Reference: The Wildlife Society Press, Washington, D.C.). \(x:\) Percentage success for mallard duck nests 56 \(\begin{array}{llll}85 & 52 & 13 & 39\end{array}\) \(y:\) Percentage success for Canada goose nests \(\begin{array}{lllll}24 & 53 & 60 & 69 & 18\end{array}\) (a) Use a calculator to verify that \(\Sigma x=245 ; \Sigma x^{2}=14,755 ; \Sigma y=224 ;\) and \(\Sigma y^{2}=12,070\) (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for \(x\), the percent of successful mallard nests. (c) Use the results of part (a) to compute the sample mean, variance, and standard deviation for \(y\), the percent of successful Canada goose nests. (d) Use the results of parts (b) and (c) to compute the coefficient of variation for successful mallard nests and Canada goose nests. Write a brief explanation of the meaning of these numbers. What do these results say about the nesting success rates for mallards compared to those of Canada geese? Would you say one group of data is more or less consistent than the other? Explain.

Consider sample data with \(\bar{x}=15\) and \(s=3\). (a) Compute the coefficient of variation. (b) Compute a \(75 \%\) Chebyshev interval around the sample mean.

How old are professional football players? The 11 th Edition of The Pro Football Encyclopedia gave the following information. Random sample of pro football player ages in years: \(\begin{array}{llllllllll}24 & 23 & 25 & 23 & 30 & 29 & 28 & 26 & 33 & 29 \\\ 24 & 37 & 25 & 23 & 22 & 27 & 28 & 25 & 31 & 29 \\ 25 & 22 & 31 & 29 & 22 & 28 & 27 & 26 & 23 & 21 \\ 25 & 21 & 25 & 24 & 22 & 26 & 25 & 32 & 26 & 29\end{array}\) (a) Compute the mean, median, and mode of the ages. (b) Interpretation Compare the averages. Does one seem to represent the age of the pro football players most accurately? Explain.
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