Beginning Statistics, 2nd Edition
Beginning Statistics, 2nd Edition
2nd Edition
ISBN: 9781932628678
Author: Carolyn Warren; Kimberly Denley; Emily Atchley
Publisher: Hawkes Learning Systems
Question
Book Icon
Chapter 3.CR, Problem 4CR
To determine

To show:

One example of a data set with large variation and one example with small variation.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given:

One data set contains large variation and one data set contains small variation.

Formula used:

The formula to calculate the mean is given as,

μ=xiN...................(1)

The formula to calculate the standard variation is,

σ2=(xiμ)2N.............(2)

Calculation:

Assume the data set of 6 observation as given below,

1,8,27,10,39,5

Substitute 1 for x1, 8 for x2, 27 for x3, 10 for x4 and 39 for x5 and 5 for x6 in equation (1),

μ=1+8+27+10+39+56=906=15

Substitute 1 for x1, 8 for x2, 27 for x3, 10 for x4 and 39 for x5, 5 for x6 and 15 for μ in equation (2),

σ2=(115)2+(815)2+(2715)2+(1015)2+(3915)2+(515)26=(14)2+(7)2+(12)2+(5)2+(24)2+(10)26=10906=181.66

Square root both sides,

σ=13.47

The standard deviation comes out to be 13.47, so, the large variance represent that the data values are more spread out.

Now, assume the data set of 6 observation as given below,

42,38,37,39,44,34

Substitute 42 for x1, 38 for x2, 37 for x3, 39 for x4 and 44 for x5 and 34 for x6 in equation (1),

μ=42+38+37+39+44+346=2346=39

Substitute 42 for x1, 38 for x2, 37 for x3, 39 for x4 and 44 for x5, 34 for x6 and 39 for μ in equation (2),

σ2=(4239)2+(3839)2+(3739)2+(3939)2+(4439)2+(3439)26=(3)2+(1)2+(2)2+(0)2+(5)2+(5)26=646=10.6

Square root both sides,

σ=3.25

The standard deviation comes out to be 3.25, so, the small variance represent that the data values are close together.

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!

Chapter 3 Solutions

Beginning Statistics, 2nd Edition

Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.CR - Prob. 1CRCh. 3.CR - Prob. 2CRCh. 3.CR - Prob. 3CRCh. 3.CR - Prob. 4CRCh. 3.CR - Prob. 5CRCh. 3.CR - Prob. 6CRCh. 3.CR - Prob. 7CRCh. 3.CR - Prob. 8CRCh. 3.CR - Prob. 9CRCh. 3.CR - Prob. 10CRCh. 3.CR - Prob. 11CRCh. 3.CR - Prob. 12CRCh. 3.CR - Prob. 13CRCh. 3.CR - Prob. 14CRCh. 3.CR - Prob. 15CRCh. 3.PA - Prob. 1PCh. 3.PA - Prob. 2PCh. 3.PA - Prob. 3PCh. 3.PA - Prob. 4PCh. 3.PA - Prob. 5PCh. 3.PA - Prob. 6PCh. 3.PA - Prob. 7PCh. 3.PA - Prob. 8PCh. 3.PA - Prob. 9PCh. 3.PA - Prob. 10PCh. 3.PB - Prob. 1PCh. 3.PB - Prob. 2PCh. 3.PB - Prob. 3PCh. 3.PB - Prob. 4P
Knowledge Booster
Background pattern image
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