Consider a sample with data values of 10, 20, 12, 17, and 16.

Measures of Location Statistics (exercises)

Aleksandra Pawłowska

April 28, 2020

Glossary (part 1)

Sample statistic A numerical value used as a summary measure for a sample (e.g. the sample mean, x̄ , the sample variance, s2, and the sample standard deviation, s). Population parameter A numerical value used as a summary measure for a population (e.g. the population mean, µ). Point estimator The sample statistic, when used to estimate the corresponding population parameter. Mean A measure of central location computed by summing the data values and dividing by the number of observations.

Aleksandra Pawłowska Measures of Location

Glossary (part 2)

Median A measure of central location provided by the value in the middle when the data are arranged in ascending order. Mode A measure of location, defined as the value that occurs with greatest frequency. Percentile A value such that at least p percent of the observations are less than or equal to this value and at least (100− p) percent of the observations are greater than or equal to this value. The 50th percentile is the median. Quartiles The 25th, 50th, and 75th percentiles, referred to as the first quartile, the second quartile (median), and third quartile, re- spectively. The quartiles can be used to divide a data set into four parts, with each part containing approximately 25% of the data.

Aleksandra Pawłowska Measures of Location

Task 1

Consider a sample with data values of 10, 20, 12, 17 and 16. Com- pute the mean and median.

Aleksandra Pawłowska Measures of Location

Task 1 – solution

Consider a sample with data values of 10, 20, 12, 17 and 16. Com- pute the mean and median. mean = x̄ = 15, median = 16

Aleksandra Pawłowska Measures of Location

Task 2

Consider a sample with data values of 10, 20, 21, 17, 16, and 12. Compute the mean and median.

Aleksandra Pawłowska Measures of Location

Task 2 – solution

Consider a sample with data values of 10, 20, 21, 17, 16, and 12. Compute the mean and median. mean = x̄ = 16, median = 16.5

Aleksandra Pawłowska Measures of Location

Task 3

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th, 25th, 65th, and 75th percentiles.

Aleksandra Pawłowska Measures of Location

Task 3 – solution

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th, 25th, 65th, and 75th percentiles.

20th percentile = 20, 25th percentile = 22.5, 65th percentile = 28, 75th percentile = 29.

Aleksandra Pawłowska Measures of Location

Task 4

Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute the mean, median, and mode.

Aleksandra Pawłowska Measures of Location

Task 4 – solution

Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute the mean, median, and mode. mean = x̄ = 59.73, median = 57, mode = 53

Aleksandra Pawłowska Measures of Location

Task 5

The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room rates for 20 cities are presented on the next slide.

1 What is the mean hotel room rate? 2 What is the median hotel room rate? 3 What is the mode? 4 What is the first quartile? 5 What is the third quartile?

Aleksandra Pawłowska Measures of Location

Aleksandra Pawłowska Measures of Location

Task 5 – solution

1 What is the mean hotel room rate? 159.05 2 What is the median hotel room rate? 161 3 What is the mode? 167 4 What is the first quartile? 136.5 5 What is the third quartile? 170

Aleksandra Pawłowska Measures of Location

Task 6

During the 2007–2008 NCAA college basketball season, men’s basketball teams attempted an all-time high number of 3-point shots, averaging 19.07 shots per game (Associated Press Sports, January 24, 2009). In an attempt to discourage so many 3-point shots and encourage more inside play, the NCAA rules commit- tee moved the 3-point line back from 19 feet, 9 inches to 20 feet, 9 inches at the beginning of the 2008–2009 basketball season. Shown in the following table are the 3-point shots taken and the 3-point shots made for a sample of 19 NCAA basketball games during the 2008–2009 season (see next slide).

1 What is the mean number of 3-point shots taken per game? 2 What is the mean number of 3-point shots made per game? 3 Using the closer 3-point line, players were making 35.2% of their shots.

What percentage of shots were players making from the new 3-point line? 4 What was the impact of the NCAA rules change that moved the 3-point

line back to 20 feet, 9 inches for the 2008–2009 season? Would you agree with the Associated Press Sports article that stated, „Moving back the 3-point line hasn’t changed the game dramatically”? Explain.

Aleksandra Pawłowska Measures of Location

Aleksandra Pawłowska Measures of Location

Task 6 – solution

1 What is the mean number of 3-point shots taken per game? 18.42

2 What is the mean number of 3-point shots made per game? 6.32

3 Using the closer 3-point line, players were making 35.2% of their shots. What percentage of shots were players making from the new 3-point line? 34.3%

4 What was the impact of the NCAA rules change that moved the 3-point line back to 20 feet, 9 inches for the 2008–2009 season? Would you agree with the Associated Press Sports article that stated, „Moving back the 3-point line hasn’t changed the game dramatically”? Explain. Yes, agree but not dramatically. Reductions of only 0.65 shots and 0.9 percentage points for made shots per game

Aleksandra Pawłowska Measures of Location

Task 7

The cost of consumer purchases such as single-family housing, gasoline, Internet services, tax preparation, and hospitalization were provided in The Wall-Street Journal (January 2, 2007). Sample data typical of the cost of tax-return prepa- ration by services such as H&R Block are:

1 Compute the mean, median, and mode. 2 Compute the first and third quartiles. 3 Compute and interpret the 90th percentile.

Aleksandra Pawłowska Measures of Location

Task 7 – solution

1 Compute the mean, median, and mode. mean = 160, median = 135, mode = 120

2 Compute the first and third quartiles. Q1 = 115, Q3 = 187.5 3 Compute and interpret the 90th percentile. 90th percentile =

245. 90% of the tax returns cost $245 or less.

Aleksandra Pawłowska Measures of Location

Applied Sciences

Architecture and Design

Biology

Business & Finance

Chemistry

Computer Science

Geography

Geology

Education

Engineering

English

Environmental science

Spanish

Government

History

Human Resource Management

Information Systems

Law

Literature

Mathematics

Nursing

Physics

Political Science

Psychology

Reading

Science

Social Science

Home

Blog

Archive

Contact

google+twitterfacebook

Copyright © 2019 HomeworkMarket.com