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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

Critical Thinking: Data Transformation In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the data set \(5,9,10,11,15\). (a) Use the defining formula, the computation formula, or a calculator to compute \(s\). (b) Add 5 to each data value to get the new data set \(10,14,15,16,20 .\) Compute \(s\). (c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set \(5,9,10,11,15 .\) (a) Use the defining formula, the computation formula, or a calculator to com- pute \(s .\) (b) Multiply each data value by 5 to obtain the new data set \(25,45,50,55,75\). Compute s. (c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant \(c\) ? (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be \(s=3.1\) miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? Given 1 mile \(=1.6\) kilometers, what is the standard deviation in kilometers?

When a distribution is mound-shaped symmetrical, what is the general relationship among the values of the mean, median, and mode?

In this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. Consider the data set \(2,2,3,6,10\). (a) Compute the mode, median, and mean. (b) Multiply each data value by \(5 .\) Compute the mode, median, and mean. (c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by the same constant? (d) Suppose you have information about average heights of a random sample of airplane passengers. The mode is 70 inches, the median is 68 inches, and the mean is 71 inches. To convert the data into centimeters, multiply each data value by \(2.54\). What are the values of the mode, median, and mean in centimeters?

At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were \(\begin{array}{rrrrrrrrrr}23 & 2 & 5 & 14 & 25 & 36 & 27 & 42 & 12 & 8 \\ 7 & 23 & 29 & 26 & 28 & 11 & 20 & 31 & 8 & 36\end{array}\) Make a box-and-whisker plot of the data. Find the interquartile range.
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