Statistics
Statistics
4th Edition
ISBN: 9780393929720
Author: David Freedman, Robert Pisani, Roger Purves
Publisher: Norton, W. W. & Company, Inc.
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 4.6, Problem 7EE

a.

To determine

Calculate the average, the deviations from average, and the SD for given lists.

a.

Expert Solution
Check Mark

Answer to Problem 7EE

(i):

The average of the given list is 2.

The deviations from average are 3, –6, 1, –3, and 5.

The SD of the given list is 4.

(ii):

The average of the given list is –2.

The deviations from average are –3, 6, –1, 3, and –5.

The SD of the given list is 4.

Explanation of Solution

Calculation:

(i):

The average of the given list is obtained as follows:

Average=Sum of data valuesNumber of data values=54+31+75=2

Thus, the average of the given list is 2.

The deviations from average is calculated as follows:

Deviation from average = (Entry Average)

Deviation from average of 5=52=3

Deviation from average of (4)=42=6

Deviation from average of 3=32=1

Deviation from average of (1)=12=3

Deviation from average of 7=72=5

Thus, deviations from average are 3, –6, 1, –3, and 5.

The SD is obtained as follows:

SD=Sum of ((EntryAverage)2)Number of data values =(52)2+(42)2+(32)2+(12)2+(72)25=805=4

Thus, the SD of the given list is 4.

(ii):

The average of the given list is obtained as follows:

Average=Sum of data valuesNumber of data values=5+43+175=2

Thus, the average of the given list is –2.

The deviations from average are calculated as follows:

Deviation from average = (Entry Average)

Deviation from average of (5)=5+2=3

Deviation from average of 4=4+2=6

Deviation from average of (3)=3+2=1

Deviation from average of 1=1+2=3

Deviation from average of (7)=7+2=5

Thus, deviations from average are –3, 6, –1, 3, and –5.

The SD is obtained as follows:

SD=Sum of ((EntryAverage)2)Number of data values =(5+2)2+(4+2)2+(3+2)2+(1+2)2+(7+2)25=805=4

Thus, the SD of the given list is 4.

b.

To determine

Explain how the list (ii) related to list (i).

In what way the relationship carries over to the average, deviations from the average, and the SD.

b.

Expert Solution
Check Mark

Explanation of Solution

From the given lists (i) & (ii), list (ii) is obtained by changing the sign of each entry of list (i).

Hence, average of list (ii) becomes negative. The signs of deviations from the average are also changes.

Since there is no change in the sum of squares of the deviations, SD of list (ii) remains same.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Questions An insurance company's cumulative incurred claims for the last 5 accident years are given in the following table: Development Year Accident Year 0 2018 1 2 3 4 245 267 274 289 292 2019 255 276 288 294 2020 265 283 292 2021 263 278 2022 271 It can be assumed that claims are fully run off after 4 years. The premiums received for each year are: Accident Year Premium 2018 306 2019 312 2020 318 2021 326 2022 330 You do not need to make any allowance for inflation. 1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method. (b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method. 2. Comment on the differences in the reserves produced by the methods in Part 1.
Use the accompanying Grade Point Averages data to find 80%,85​%, and 99%confidence intervals for the mean GPA.   view the Grade Point Averages data. Gender    College    GPAFemale    Arts and Sciences    3.21Male    Engineering    3.87Female    Health Science    3.85Male    Engineering    3.20Female    Nursing    3.40Male    Engineering    3.01Female    Nursing    3.48Female    Nursing    3.26Female    Arts and Sciences    3.50Male    Engineering    3.00Female    Arts and Sciences    3.13Female    Nursing    3.34Female    Nursing    3.67Female    Education    3.45Female    Engineering    3.17Female    Health Science    3.28Female    Nursing    3.25Male    Engineering    3.72Female    Arts and Sciences    2.68Female    Nursing    3.40Female    Health Science    3.76Female    Arts and Sciences    3.72Female    Education    3.44Female    Arts and Sciences    3.61Female    Education    3.29Female    Nursing    3.20Female    Education    3.80Female    Business    3.26Male…
Business Discuss
Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY