Loading...

Messages

Proposals

Stuck in your homework and missing deadline? Get urgent help in $10/Page with 24 hours deadline

Get Urgent Writing Help In Your Essays, Assignments, Homeworks, Dissertation, Thesis Or Coursework & Achieve A+ Grades.

Privacy Guaranteed - 100% Plagiarism Free Writing - Free Turnitin Report - Professional And Experienced Writers - 24/7 Online Support

Data collected over several time periods are

16/10/2021 Client: muhammad11 Deadline: 2 Day

Statistics

Measures of Distribution Shape and Detecting Outliers

Statistics (exercises)

Aleksandra Pawłowska

May 19, 2020

Glossary

Skewness A measure of the shape of a data distribution. Data skewed to the left result in negative skewness; a symmetric data distribution results in zero skewness; and data skewed to the right result in positive skewness. z-score A value computed by dividing the deviation about the mean (xi − x̄) by the standard deviation s. A z-score is referred to as a standardized value and denotes the number of standard deviations xi is from the mean. Chebyshev’s theorem A theorem that can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean. Empirical rule A rule that can be used to compute the percentage of data values that must be within one, two, and three standard deviations of the mean for data that exhibit a bell-shaped distribution. Outlier An unusually small or unusually large data value.

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 1

Consider a sample with data values of 10, 20, 12, 17, and 16. Com- pute the z-score for each of the five observations.

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 1 – solution

Consider a sample with data values of 10, 20, 12, 17, and 16. Com- pute the z-score for each of the five observations. z1 = −1.25, z2 = 1.25, z3 = −0.75, z4 = 0.5, z5 = 0.25

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 2

Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 520, 650, 500, 450, and 280?

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 2 – solution

Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 520, 650, 500, 450, and 280? z1 = 0.2, z2 = 1.5, z3 = 0, z4 = −0.5, z5 = −2.2

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 3

Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev’s theorem to determine the percentage of the data within each of the following ranges:

1 20 to 40 2 15 to 45 3 22 to 38 4 18 to 42 5 12 to 48

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 3 – solution

1 20 to 40 75% 2 15 to 45 89% 3 22 to 38 61% 4 18 to 42 83% 5 12 to 48 92%

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 4

Suppose the data have a bell-shaped distribution with a mean of 30 and a standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges:

1 20 to 40 2 15 to 45 3 25 to 35

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 4 – solution

1 20 to 40 95% 2 15 to 45 almost 100% 3 25 to 35 68%

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 5

The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.2 hours.

1 Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours.

2 Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours.

3 Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours per day. How does this result compare to the value that you obtained using Chebyshev’s theorem in part (a)?

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 5 – solution

1 Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours. 75%

2 Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours. 84%

3 Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours per day. How does this result compare to the value that you obtained using Chebyshev’s theorem in part (1)? 95%; if we assume, that data are distributed symetrically, then more observations are closer to the mean

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 6

The Energy Information Administration reported that the mean re- tail price per gallon of regular grade gasoline was $2.05 (Energy Information Administration, May 2009). Suppose that the standard deviation was $0.10 and that the retail price per gallon has a bell- shaped distribution.

1 What percentage of regular grade gasoline sold between $1.95 and $2.15 per gallon?

2 What percentage of regular grade gasoline sold between $1.95 and $2.25 per gallon?

3 What percentage of regular grade gasoline sold for more than $2.25 per gallon?

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 6 – solution

1 What percentage of regular grade gasoline sold between $1.95 and $2.15 per gallon? 68%

2 What percentage of regular grade gasoline sold between $1.95 and $2.25 per gallon? 81.5%

3 What percentage of regular grade gasoline sold for more than $2.25 per gallon? 2.5%

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 7

The national average for the math portion of the College Board’s Scholastic Aptitude Test (SAT) is 515 (The World Almanac, 2009). The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the verbal test scores.

1 What percentage of students have an SAT verbal score greater than 615?

2 What percentage of students have an SAT verbal score greater than 715?

3 What percentage of students have an SAT verbal score between 415 and 515?

4 What percentage of students have an SAT verbal score between 315 and 615?

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Task 7 – solution

1 What percentage of students have an SAT verbal score greater than 615? 16%

2 What percentage of students have an SAT verbal score greater than 715? 2.5%

3 What percentage of students have an SAT verbal score between 415 and 515? 34%

4 What percentage of students have an SAT verbal score between 315 and 615? 81.5%

Aleksandra Pawłowska Measures of Distribution Shape and Detecting Outliers

Homework is Completed By:

Writer Writer Name Amount Client Comments & Rating
Instant Homework Helper

ONLINE

Instant Homework Helper

$36

She helped me in last minute in a very reasonable price. She is a lifesaver, I got A+ grade in my homework, I will surely hire her again for my next assignments, Thumbs Up!

Order & Get This Solution Within 3 Hours in $25/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 3 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

Order & Get This Solution Within 6 Hours in $20/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 6 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

Order & Get This Solution Within 12 Hours in $15/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 12 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

6 writers have sent their proposals to do this homework:

Engineering Exam Guru
Financial Analyst
Instant Homework Helper
Write My Coursework
Finance Master
Assignment Guru
Writer Writer Name Offer Chat
Engineering Exam Guru

ONLINE

Engineering Exam Guru

After reading your project details, I feel myself as the best option for you to fulfill this project with 100 percent perfection.

$47 Chat With Writer
Financial Analyst

ONLINE

Financial Analyst

I can assist you in plagiarism free writing as I have already done several related projects of writing. I have a master qualification with 5 years’ experience in; Essay Writing, Case Study Writing, Report Writing.

$27 Chat With Writer
Instant Homework Helper

ONLINE

Instant Homework Helper

I am an elite class writer with more than 6 years of experience as an academic writer. I will provide you the 100 percent original and plagiarism-free content.

$28 Chat With Writer
Write My Coursework

ONLINE

Write My Coursework

Being a Ph.D. in the Business field, I have been doing academic writing for the past 7 years and have a good command over writing research papers, essay, dissertations and all kinds of academic writing and proofreading.

$46 Chat With Writer
Finance Master

ONLINE

Finance Master

I am an academic and research writer with having an MBA degree in business and finance. I have written many business reports on several topics and am well aware of all academic referencing styles.

$50 Chat With Writer
Assignment Guru

ONLINE

Assignment Guru

I am a professional and experienced writer and I have written research reports, proposals, essays, thesis and dissertations on a variety of topics.

$47 Chat With Writer

Let our expert academic writers to help you in achieving a+ grades in your homework, assignment, quiz or exam.

Similar Homework Questions

Leadership and Change in organization - Regular practices of the jains include - John locke psychology tabula rasa - Presentation Script regards media industry concentration --- Due ASAP - The class game by mary casey analysis - Which of the following statements about ethics audits is false - The work wes moore chapter summary - 6es7 392 1am00 0aa0 wiring - What privileges are afforded to accounts with desktop user privileges? - Recommendation report sample in technical writing - Internal environment analysis example - Finding limits algebraically worksheet - Cognitive enhancement therapy techniques - Unisa late submission of assignments - Career development assessment and counseling model - The language of baklava chapter summary - David deangelo on being a man download - Suicide silence the cleansing zip - Discussion - Employment law advice nsw - Safe work industry module - Nacionaline dailes galerija kavine - What is a dress up in writing - Epicurus reader pdf - Convert 440 yards to meters - How to find remaining zeros - Due today - Monotype corsiva history - Group therapy - How to make a mousetrap car step by step - MKT 630 IP2 - You have $10000 to invest in a stock portfolio - Week 4 Report - Sota instruments model zbb5 ionic silver generator - Is devondale cheese halal certified - What is personal beliefs - How to find your gpa rmit - Cranleigh gardens medical centre - Atc 710 flight simulator - Wilsons prom northern circuit - Limavady past and present - Cyber Security - A3 a4 a5 paper size - Becoming a master manager a competing values approach 6th edition - Dulux heritage colours exterior australia - Humber bay shores master plan - Trinity beach driving school - Gordon rule essay - Astable multivibrator using 555 timer calculator - N491 Assignment Mod 6: case study - The heavenly christmas tree pdf - Dulux crisp linen 61yy 89 040 - Block style business letter template word - History of nurse anesthesia - How to read literature like a professor chapter main points - Private label production bsg - Illinois agility test norms - A sharecropping contract 1866 voices of freedom - Vsim skyler hansen answers - Where did martha stewart work before entrepreneur - W9PAD530 - Leadership and management models mgt 410 - Research - Adf assessment day medical - Markel m 2015 technical communication 11th ed - Please hel with Anatomy and Physiology - Abs blink codes wabco - Economics 1 - Plum pudding model labeled - Precipitating calcium carbonate lab report - Discussion - Definition of equivalence in translation - Tutorial questions-Marketing research - How many degrees of freedom do monatomic gases have - Webography - Boy's life by howard korder script - Identify a reform that took place during the Progressive era. This could include Constitutional amendments, movements among women or laborers, changes in technology, changes in family structure, and changes in laws. - Calgary paper company produces paper for photocopiers - Essay(900 words) - Balanced unbalanced forces worksheet - One art by elizabeth bishop - Accounting - Write a journal about Muslim countries - Allinson and hayes cognitive style index questionnaire - How to write a metanarrative - The girl who loved tom gordon chapter 1 summary - Deterministic vs stochastic model - What are two examples of hypothetical syllogism - Mater christi catholic church yangebup - Industrial and organizational behavior 6th edition - Types of power in social work - Module 2 - Current Events 2 - Axial flow fan performance curve - Abc jackson five video - Health communication - St gabriels church prestonpans - Investor presentation - Tesla case study strategic management - Information Security Laws - Boston consulting group matrix