/*! 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 66 The five-number summary for a di... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 66

The five-number summary for a distribution of final exam scores is $$ 60,78,80,90,100 $$ Is it possible to draw a boxplot based on this information? Why or why not?

Short Answer

Expert verified
Yes, it is possible to draw a boxplot from this information because it gives us the minimum, first quartile, median, third quartile and maximum of the distribution. As per these five pieces of information, none of the higher quartiles are less than the lower ones which validates the possibility of drawing a boxplot.

Step by step solution

01

Understanding what a Boxplot is

A boxplot is a standardized way of displaying the distribution of data based on a five number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum). It is also known as a box and whisker plot and it's used in descriptive statistics.
02

Checking the provided Five-Number Summary

Looking at the provided data, we have 5 numbers, which should correspond to minimum, Q1, median, Q3, and maximum.
03

Validate if the Five-Number Summary is Correct

There are some rules that should be followed by the five-number summary. Specifically, the minimum should be less than Q1, Q1 should be less than the median, the median should be less than Q3, and Q3 should be less than the maximum. In this case, all conditions are achieved: 60 < 78 < 80 < 90 < 100.
04

Draw the Boxplot

The boxplot can be drawn with a box from Q1 to Q3 (78 to 90 in this case) with a line indicating the median (80). The whiskers extend from the box to the minimum and maximum values (60 and 100).

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

Construct two sets of numbers with at least five numbers in each set (showing them as dotplots) with the following characteristics: The mean of set \(A\) is larger than that of set \(B\), but the median of set \(\mathrm{B}\) is larger than the median of set \(\mathrm{A}\). Label each dotplot with its mean and median in the correct place.

This list represents the numbers of paid vacation days required by law for different countries. (Source: 2009 World Almanac and Book of Facts) $$ \begin{array}{|l|l|} \hline \text { United States } & 0 \\ \hline \text { Australia } & 20 \\ \hline \text { Italy } & 20 \\ \hline \text { France } & 30 \\ \hline \text { Germany } & 24 \\ \hline \text { Canada } & 10 \\ \hline \end{array} $$ a. Find the mean, rounding to the nearest tenth of a day. Interpret the mean in this context. Report the mean in a sentence that includes words such as "paid vacation days." b. Find the standard deviation, rounding to the nearest tenth of a day. Interpret the standard deviation in context. c. Which number of days is farthest from the mean and therefore contributes most to the standard deviation?

The teachers of a school collected data on the self-reported numbers of sick leaves taken by students in the months of September and October. $$ \begin{aligned} &\text { September: } 8,3,2,1,6,4,1,8,2,2,2,5,7,1,8,9 \text { , } \\ &\qquad 4,3,2,6,8,1,3,9,8,1,1,12,9,10 \end{aligned} $$ $$ \begin{aligned} &\text { October: } 2,8,3,6,1,5,4,9,8,1,1,12,9,9,0,6,1,8 \text { , } \\ &4,2,1,9,12,8,1,3,2,4,7,1 \end{aligned} $$ a. Compare the means in a sentence or two. b. Compare the standard deviation in a sentence or two.

Babies born after 40 weeks gestation have a mean length of \(52.2\) centimeters (about \(20.6\) inches). Babies born one month early have a mean length of \(47.4 \mathrm{~cm}\). Assume both standard deviations are \(2.5 \mathrm{~cm}\) and the distributions are unimodal and symmetric. (Source: www.babycenter.com) a. Find the standardized score (z-score), relative to all U.S. births, for a baby with a birth length of \(45 \mathrm{~cm}\). b. Find the standardized score of a birth length of \(45 \mathrm{~cm}\) for babies born one month early, using \(47.4\) as the mean. c. For which group is a birth length of \(45 \mathrm{~cm}\) more common? Explain what that means.

The monthly salaries of qualified professionals have a mean of $$\$ 50,000$$ and a standard deviation of $$\$ 20,000$$, while those of semi-qualified professionals have a mean of $$\$ 29,000$$ and a standard deviation of $$\$ 3,500$$. Assuming both types of salaries have distributions that are unimodal and symmetric, which is more unusual: a qualified professional having a salary of $$\$ 80,000$$ or a semi-qualified professional having a salary of $$\$ 36,000 ?$$ Show your work.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

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.