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91Ó°ÊÓ

Angela took a general aptitude test and scored in the 82 nd percentile for aptitude in accounting. What percentage of the scores were at or below her score? What percentage were above?

Short Answer

Expert verified
82% were at or below her score; 18% were above.

Step by step solution

01

Understanding Percentiles

A percentile tells us the percentage of scores that fall below a certain point. In this case, Angela scored in the 82nd percentile, meaning 82% of the scores are below her score.
02

Calculating Scores Below

Since Angela is in the 82nd percentile, this directly means that 82% of the scores were below her score.
03

Finding Scores Above

To find the percentage of scores above Angela's, subtract the percentile from 100%. Therefore, 100% - 82% = 18%. So, 18% of the scores are above her score.

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Key Concepts

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

Percentage Calculation
Understanding how to calculate percentages is an essential skill, especially in contexts like evaluating test scores or analyzing data. A percentage is a way to express a number as a fraction of 100. For example, if someone says "82%," it means 82 out of every 100.

Calculating percentages involves simple arithmetic operations like multiplication and division. Here's a quick breakdown of the process:
  • To find a certain percentage of a number, multiply the number by the percentage (in decimal form). For example, 20% of 50 is calculated as 50 x 0.20 = 10.
  • To calculate what percentage one number is of another, divide the first number by the second and then multiply by 100. For example, if you scored 45 out of 50 on a test, the calculation would be (45 ÷ 50) x 100 = 90%.
Understanding these basic percentage calculations will help in interpreting such values in various contexts, like interpreting aptitude test results.
Aptitude Test
An aptitude test is designed to evaluate a person's ability to perform specific tasks or react to different scenarios. These kinds of tests are standardized and often used to determine competence in different fields such as reasoning, logic, or specific subjects like math or language.

The scores of aptitude tests are usually expressed in percentiles. This makes it easier to compare an individual's performance against a larger group. For example, if Angela scores in the 82nd percentile, it means she performed better than 82% of participants. Percentiles are crucial in understanding relative performance rather than just absolute scores.

Aptitude tests are commonly used in education, career assessments, and even in competitive job recruitment processes. These tests often aim to identify the strengths and weaknesses of individuals in a formal and systematic way. Understanding how to approach these tests by improving fundamental skills can significantly impact one's career and educational trajectory.
Score Distribution
Score distribution in the context of aptitude tests refers to how all participants' scores are spread across different values. When we talk about distribution, we are essentially looking at a visual or statistical way of representing the frequency of all the possible scores.

Typically, score distributions can offer insights into the overall difficulty of a test. For example:
  • A test where most participants score similarly will have a narrow and peaked distribution, suggesting evenly matched difficulty for a group.
  • A more spread-out distribution may indicate varied levels of understanding among test-takers, or it could reflect differentiated levels of test question difficulty.
In Angela’s case, her 82nd percentile ranking means she scored higher than a large part of the score distribution. This simply indicates that her aptitude in the tested area is better than most.

Analyzing score distribution helps educators and test designers create fair and effective assessments by balancing the level of challenge and ensuring it differentiates between varying skill levels among participants.

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Most popular questions from this chapter

In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth \(25 \%\) of your total grade, each major test is worth \(22.5 \%\), and the final exam is worth \(30 \%\). Compute the weighted average for the following scores: 92 on the lab, 81 on the first major test, 93 on the second major test, and 85 on the final exam.

Consider the following ordered data: \(\begin{array}{ccccccccc}2 & 5 & 5 & 6 & 7 & 7 & 8 & 9 & 10\end{array}\) (a) Find the low, \(Q_{1}\), median, \(Q_{3}\), high. (b) Find the interquartile range. (c) Make a box-and-whisker plot.

Do bonds reduce the overall risk of an investment portfolio? Let \(x\) be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let \(y\) be a random variable representing annual return for Vanguard Balanced Index \((60 \%\) stock and \(40 \%\) bond). For the past several years, we have the following data (Reference: Morningstar Research Group, Chicago). \(\begin{array}{llllllllrr}x: & 11 & 0 & 36 & 21 & 31 & 23 & 24 & -11 & -11 & -21 \\ y: & 10 & -2 & 29 & 14 & 22 & 18 & 14 & -2 & -3 & -10\end{array}\) (a) Compute \(\Sigma x, \Sigma x^{2}, \Sigma y\), and \(\Sigma y^{2}\). (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for \(x\) and for \(y\). (c) Compute a \(75 \%\) Chebyshev interval around the mean for \(x\) values and also for \(y\) values. Use the intervals to compare the two funds. (d) Compute the coefficient of variation for each fund. Use the coefficients of variation to compare the two funds. If \(s\) represents risks and \(\bar{x}\) represents expected return, then \(s / \bar{x}\) can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller \(C V\) better? Explain.

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 adding the same number to each data value. Consider the data set \(2,2,3,6,10\). (a) Compute the mode, median, and mean. (b) Add 5 to each of the data values. 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 the same constant is added to each data value in a set?

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