/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 68 Explain the concept of the perce... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 68

Explain the concept of the percentile rank for an observation of a data set.

Short Answer

Expert verified
The percentile rank of a data set observation is the percentage of data lower or equal to that observation. To calculate it, arrange the data set in ascending order, identify the position of the observation and use the formula provided to calculate the percentile rank. For instance, the percentile rank of 30 in the data set {10, 20, 30, 40, 50} is 60%.

Step by step solution

01

Understand the Percentile Rank Concept

The percentile rank of an observation is the percentage of data in a data set that is less than or equal to that observation. It provides a way to compare an individual value with the rest of the data set. It is often used in different fields such as statistics, academia, and business.
02

Calculate the Percentile Rank

To calculate the percentile rank, first arrange the data set in ascending order. Then, identify the position of the observation in question. Following that, use the formula: \( \text{{Percentile rank}} = \frac{{\text{{number of scores less than the target score}} + 0.5 \times \text{{number of scores equal to the target score}}}}{\text{{total number of scores}}} \times 100 \)
03

Providing an Example

For example, if you have a data set {10, 20, 30, 40, 50} and you want to find the percentile rank of 30, first, arrange the data set. It is already in ascending order. The position of 30 is 3, and the total number of scores is 5. Following the formula, the percentile rank is \( \frac{{2 + 0.5 \times 1}}{5} \times 100 = 60 \). Hence, 60% of the scores are less than or equal to 30.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Is it possible for a (quantitative) data set to have no mean, no median, or no mode? Give an example of a data set for which this summary measure does not exist.

Which of the five measures of center (the mean, the median, the trimmed mean, the weighted mean, and the mode) can be calculated for quantitative data only, and which can be calculated for both quantitative and qualitative data? Illustrate with examples.

The following data give the annual salaries (in thousand dollars) of 20 randomly selected health care workers. \(\begin{array}{llllllllll}50 & 71 & 57 & 39 & 45 & 64 & 38 & 53 & 35 & 62 \\\ 74 & 40 & 67 & 44 & 77 & 61 & 58 & 55 & 64 & 59\end{array}\) a. Compute the range, variance, and standard deviation for these data. b. Calculate the coefficient of variation. c. Are the values of these summary measures population parameters or sample statistics? Explain.

The following data give the total food expenditures (in dollars) for the past one month for a sample of 20 families. \(\begin{array}{rrrrrrrrrr}1125 & 530 & 1234 & 595 & 427 & 872 & 1480 & 699 & 1274 & 1187 \\ 933 & 1127 & 716 & 1065 & 934 & 1630 & 1046 & 2199 & 1353 & 441\end{array}\) Prepare a box-and-whisker plot. Is the distribution of these data symmetric or skewed? Are there any outliers? If so, classify them as mild or extreme.

The following data represent the systolic blood pressure reading (that is, the top number in the standard blood pressure reading) in \(\mathrm{mmHg}\) for each of 20 randomly selected middle-aged males who were taking blood pressure medication. \(\begin{array}{llllllllll}139 & 151 & 138 & 153 & 134 & 136 & 141 & 126 & 109 & 144\end{array}\) \(\begin{array}{llllllllll}111 & 150 & 107 & 132 & 144 & 116 & 159 & 12.1 & 127 & 113\end{array}\) a. Calculate the mean, median, and mode for these data. b. Calculate the \(10 \%\) trimmed mean for these data.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.