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Chapter 3: Problem 2

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

Short Answer

Expert verified
The minimal percentile rank for a successful applicant is the 75th percentile.

Step by step solution

01

Understanding Percentiles and Quartiles

The term 'upper quartile' refers to the top 25% of a data set. In percentile terms, this means that a student must be in the 75th percentile or higher to be considered among the upper quartile. Percentiles allow us to compare scores or ranks by determining the percentage of a distribution that is below a certain value.
02

Identify the Minimum Percentile for Upper Quartile

Since being in the upper quartile means being at or above the 75th percentile, a student must at least rank in the 75th percentile among their graduating class. This percentile mark is the threshold for being in the top 25% of a class.
03

Conclusion and Application

To meet the standard for admission to Redfield College, an applicant should rank at least in the 75th percentile of their class. This percentile rank guarantees that they are in the upper quartile, meeting the admission requirements.

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Key Concepts

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

Understanding Quartiles
Quartiles are values that divide a data set into four equal parts, making it easier to understand the distribution of data.
This division helps in analyzing the spread, central tendency, and outliers.
  • The first quartile (Q1), also known as the lower quartile, marks the 25th percentile. It separates the lowest 25% of the data from the rest.
  • The second quartile (Q2) is the median of the data and represents the 50th percentile.
  • The third quartile (Q3), or upper quartile, is at the 75th percentile, leaving only the top 25% of data above this point.
The upper quartile is the range we look at when determining students who are performing in the top quarter.
College Admissions Criteria
Colleges often use various criteria to evaluate applicants and select students who will thrive in their programs.
Aside from grades, they may consider aspects like test scores, extracurricular activities, and personal essays. But academic rank is a significant factor too, which is where quartiles and percentiles come into play.
  • Being in the upper quartile implies a student ranks within at least the top 25% of their class.
  • This ranking is usually critical for colleges aiming to maintain high academic standards among incoming students.
For example, Redfield College requires students to be in the upper quartile for admissions, meaning they should have a percentile rank of 75 or above.
What is Percentile Rank?
The percentile rank of a number tells you what percentage of scores are below that particular value in a data set.
This statistic helps in understanding where an individual stands relative to others.
  • A student at the 75th percentile has performed better than 75% of their peers.
  • Percentiles essentially provide a way to understand a student鈥檚 performance in context, allowing comparison with a broader group.
This is crucial for college applications as it allows institutions to quantitatively assess student performance across different schools and districts.
Demystifying the Upper Quartile
The upper quartile, also known as the third quartile, is a term that resonates highly during admissions because it signifies excellence.
As it represents the top 25% of a group, it is often used as a cutoff for competitive situations.
  • Being in the upper quartile means that an individual鈥檚 performance or position is better than the majority of their peers.
  • This metric is essential for schools like Redfield College to identify strong candidates who are likely to excel academically.
For applicants, achieving a rank in the upper quartile ensures they meet the minimum academic criteria set by such institutions, hence improving their chances of acceptance.

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Most popular questions from this chapter

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) Compare the averages. Does one seem to represent the age of the pro football players most accurately? Explain.

How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures \(\left({ }^{\circ} \mathrm{F}\right)\) were taken from May to November in the vicinity of Furnace Creek. \(\begin{array}{lllllll}146 & 152 & 168 & 174 & 180 & 178 & 179 \\ 180 & 178 & 178 & 168 & 165 & 152 & 144\end{array}\) Compute the mean, median, and mode for these ground temperatures.

Kevlar epoxy is a material used on the NASA Space Shuttle. Strands of this epoxy were tested at the \(90 \%\) breaking strength. The following data represent time to failure (in hours) for a random sample of 50 epoxy strands (Reference: \(\mathrm{R} . \mathrm{E} .\) Barlow, University of California, Berkeley). Let \(x\) be a random variable representing time to failure (in hours) at \(90 \%\) breaking strength. Note: These data are also available for download online in HM StatSPACETM. \(\begin{array}{llllllllll}0.54 & 1.80 & 1.52 & 2.05 & 1.03 & 1.18 & 0.80 & 1.33 & 1.29 & 1.11 \\ 3.34 & 1.54 & 0.08 & 0.12 & 0.60 & 0.72 & 0.92 & 1.05 & 1.43 & 3.03 \\ 1.81 & 2.17 & 0.63 & 0.56 & 0.03 & 0.09 & 0.18 & 0.34 & 1.51 & 1.45 \\ 1.52 & 0.19 & 1.55 & 0.02 & 0.07 & 0.65 & 0.40 & 0.24 & 1.51 & 1.45 \\ 1.60 & 1.80 & 4.69 & 0.08 & 7.89 & 1.58 & 1.64 & 0.03 & 0.23 & 0.72\end{array}\) (a) Find the range. (b) Use a calculator to verify that \(\Sigma x=62.11\) and \(\Sigma x^{2}=164.23\). (c) Use the results of part (b) to compute the sample mean, variance, and standard deviation for the time to failure. (d) Use the results of part (c) to compute the coefficient of variation. What does this number say about time to failure? Why does a small CV indicate more consistent data, whereas a larger CV indicates less consistent data? Explain.

Leisure: Maui Vacation How expensive is Maui? If you want a vacation rental condominium (up to four people), visit the Brase/Brase statistics site, find the link to Maui, and then search for accommodations. The Maui News gave the following costs in dollars per day for a random sample of condominiums located throughout the island of Maui. \(\begin{array}{llrlllllll}89 & 50 & 68 & 60 & 375 & 55 & 500 & 71 & 40 & 350 \\ 60 & 50 & 250 & 45 & 45 & 125 & 235 & 65 & 60 & 130\end{array}\) (a) Compute the mean, median, and mode for the data. (b) Compute a \(5 \%\) trimmed mean for the data, and compare it with the mean computed in part (a). Does the trimmed mean more accurately reflect the general level of the daily rental costs? (c) If you were a travel agent and a client asked about the daily cost of renting a condominium on Maui, what average would you use? Explain. Is there any other information about the costs that you think might be useful, such as the spread of the costs?

Pax World Balanced is a highly respected, socially responsible mutual fund of stocks and bonds (see Viewpoint). Vanguard Balanced Index is another highly regarded fund that represents the entire U.S. stock and bond market (an index fund). The mean and standard deviation of annualized percent returns are shown below. The annualized mean and standard deviation are based on the years 1993 through 2002 (Source: Morningstar). Pax World Balanced: \(\bar{x}=9.58 \% ; s=14.05 \%\) Vanguard Balanced Index: \(\bar{x}=9.02 \% ; s=12.50 \%\) (a) Compute the coefficient of variation for each fund. If \(\bar{x}\) represents return and \(s\) represents risk, then explain why the coefficient of variation can be taken to represent risk per unit of return. From this point of view, which fund appears to be better? Explain. (b) Compute a \(75 \%\) Chebyshev interval around the mean for each fund. Use the intervals to compare the two funds. As usual, past performance does not guarantee future performance.
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