In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 15, 5, 6, 14, 16. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to four decimal places.) s = (b) Multiply each data value by 7 to obtain the new data set 105, 35, 42, 98, 112. Compute s. (Round your answer to four decimal places.) s = (c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c? - Multiplying each data value by the same constant c results in the standard deviation remaining the same. - Multiplying each data value by the same constant c results in the standard deviation increasing by c units. - Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. - Multiplying each data value by the same constant c results in the standard deviation being |c| times as large.
In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 15, 5, 6, 14, 16. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to four decimal places.) s = (b) Multiply each data value by 7 to obtain the new data set 105, 35, 42, 98, 112. Compute s. (Round your answer to four decimal places.) s = (c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c? - Multiplying each data value by the same constant c results in the standard deviation remaining the same. - Multiplying each data value by the same constant c results in the standard deviation increasing by c units. - Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. - Multiplying each data value by the same constant c results in the standard deviation being |c| times as large.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 15, 5, 6, 14, 16.
(a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to four decimal places.)
s =
(b) Multiply each data value by 7 to obtain the new data set 105, 35, 42, 98, 112. Compute s. (Round your answer to four decimal places.)
s =
(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c?
Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)
s = km
s =
(b) Multiply each data value by 7 to obtain the new data set 105, 35, 42, 98, 112. Compute s. (Round your answer to four decimal places.)
s =
(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c?
- Multiplying each data value by the same constant c results in the standard deviation remaining the same.
- Multiplying each data value by the same constant c results in the standard deviation increasing by c units.
- Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller.
- Multiplying each data value by the same constant c results in the standard deviation being |c| times as large.
Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)
s = km
Transcribed Image Text:In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 15, 5, 6, 14, 16.
n USE SALT
(a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to four decimal places.)
S =
(b) Multiply each data value by 7 to obtain the new data set 105, 35, 42, 98, 112. Compute s. (Round your answer to four decimal places.)
S =
(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c?
O Multiplying each data value by the same constant c results in the standard deviation remaining the same.
O Multiplying each data value by the same constant c results in the standard deviation increasing by c units.
O Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller.
O Multiplying each data value by the same constant c results in the standard deviation being |c| times as large.
(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.1 miles. Your friend wants to know the standard deviation in
kilometers. Do you need to redo all the calculations?
O Yes
O No
Given 1 mile = 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)
S =
X km
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman