/*! 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 88 Briefly describe how the percent... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 88

Briefly describe how the percentiles are calculated for a data set.

Short Answer

Expert verified
Percentiles in a data set are calculated by first arranging the data in ascending order. The rank is then computed using the formula \( R = P/100 * (N + 1) \), where \( P \) is the desired percentile and \( N \) is the total number of elements in the set. If the rank is not an integer, the percentile value is calculated by interpolating between the two values at the indices obtained by rounding the rank up and down. If the rank is an integer, the percentile is the value at that rank.

Step by step solution

01

Arrange the Data in Ascending Order

To begin with, arrange the data points in your set in increasing order. This means, the smallest value first and the largest value last. For example, if you have the data points \( [7, 15, 3, 9] \), the sorted data set would look like \( [3, 7, 9, 15] \). This step is crucial as it aids in determining the position of a value in the set more clearly.
02

Compute the Rank

After sorting the data, you need to compute the 'Rank'. The Rank identifies the place of a data point in the data set. It is calculated using the formula: \( R = P/100 * (N + 1) \), where \( P \) is the desired percentile and \( N \) is the total number of data in your set. For instance, if you want to calculate the 30th percentile for a data set containing 10 points, the rank will be \( R = 30/100 * (10 + 1) = 3.3 \).
03

Find the Percentile

Finally, to find the percentile of your desired rank, if the rank is not an integer, round it down to get the index of the first value (lets call it \( V1 \)), and round it up to get the index of the second value (call it \( V2 \)). The percentile is then found by interpolating between \( V1 \) and \( V2 \). If the rank is an integer, the percentile is the value at that rank. For example, based on the computed rank from the previous step, our V1 is the value at index 3 and V2 is the value at index 4. To get the 30th percentile, we interpolate between the two: \( 30th percentile = V1 + (R - floor(R)) * (V2 - V1) \). This gives us the value of the 30th percentile.

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

The mean monthly mortgage paid by all home owners in a town is \(\$ 2365\) with a standard deviation of \(\$ 340\). a. Using Chebyshev's theorem, find at least what percentage of all home owners in this town pay a monthly mortgage of i. \(\$ 1685\) to \(\$ 3045\) ii. \(\$ 1345\) to \(\$ 3385\) "b. Using Chebyshev's theorem, find the interval that contains the monthly mortgage payments of at least \(84 \%\) of all home owners in this town.

Briefly describe how the three quartiles are calculated for a data set. Illustrate by calculating the three quartiles for two examples, the first with an odd number of observations and the second with an even number of observations.

Each year the faculty at Metro Business College chooses 10 members from the current graduating class that they feel are most likely to succeed. The data below give the current annual incomes (in thousands of dollars) of the 10 members of the class of 2004 who were voted most likely to succeed. \(\begin{array}{lllllllll}59 & 68 & 84 & 78 & 107 & 382 & 56 & 74 & 97 & 60\end{array}\) a. Calculate the mean and median. b. Does this data set contain any outlier(s)? If yes, drop the outlier(s) and recalculate the mean and median. Which of these measures changes by a greater amount when you drop the outlier(s)? C. Is the mean or the median a better summary measure for these data? Explain.

For any data, the sum of all values is equal to the product of the sample size and mean; that is, \(\Sigma x=n \bar{x}\). Suppose the average amount of money spent on shopping by 10 persons during a given week is \(\$ 105.50\). Find the total amount of money spent on shopping by these 10 persons.

The heights of five starting players on a basketball team have a mean of 76 inches, a median of 78 inches, and a range of 11 inches. a. If the tallest of these five players is replaced by a substitute who is 2 inches taller, find the new mean, median, and range. b. If the tallest player is replaced by a substitute who is 4 inches shorter, which of the new values (mean, median, range) could you determine, and what would their new values be?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

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.