Consider the following four data sets in the table below. Complete parts (a) through (g) below. E Click the icon to view the four data sets. Data Set I Data Set Il Data Set III Data Set IV Range (Set I) = 8 Range (Set II) = 0 9 5 2 4 1 7 9 5 4 4 Range (Set III) = 8 = 8 Range (Set IV) (Type integers or decimals. Do not round.) 3 1 9 5 4 9 9 5 10 4 9 1 9 4 10 e. Use the defining formula compute the sample standard deviation of each data set. s (Set I) = s (Set II) Print Done s (Set III) s (Set IV) = (Type integers or decimals. Round to one decimal place as needed.) f. From your answers to parts (d) and (e), which measure variation better distinguishes the spread in the four data sets: the range or the standard deviation? Explain your answer. O A. The standard deviation distinguishes spread better because it shows that the sets are structurally different, despite having similar ranges and means. O B. The standard deviation distinguishes spread better because it is resistant to outliers, and is therefore more robust than the range. OC. The range distinguishes spread better because it shows that having different standard deviations doesn't imply that the means must be different. O D. The range distinguishes spread better because it shows that the sets are structurally similar, because their extrema are equally spread out.
Consider the following four data sets in the table below. Complete parts (a) through (g) below. E Click the icon to view the four data sets. Data Set I Data Set Il Data Set III Data Set IV Range (Set I) = 8 Range (Set II) = 0 9 5 2 4 1 7 9 5 4 4 Range (Set III) = 8 = 8 Range (Set IV) (Type integers or decimals. Do not round.) 3 1 9 5 4 9 9 5 10 4 9 1 9 4 10 e. Use the defining formula compute the sample standard deviation of each data set. s (Set I) = s (Set II) Print Done s (Set III) s (Set IV) = (Type integers or decimals. Round to one decimal place as needed.) f. From your answers to parts (d) and (e), which measure variation better distinguishes the spread in the four data sets: the range or the standard deviation? Explain your answer. O A. The standard deviation distinguishes spread better because it shows that the sets are structurally different, despite having similar ranges and means. O B. The standard deviation distinguishes spread better because it is resistant to outliers, and is therefore more robust than the range. OC. The range distinguishes spread better because it shows that having different standard deviations doesn't imply that the means must be different. O D. The range distinguishes spread better because it shows that the sets are structurally similar, because their extrema are equally spread out.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Data Sets
Consider the following four data sets in the table below. Complete parts (a) through (g) below.
Click the icon to view the four data sets.
Data Set I
Data Set II
Data Set III
Data Set IV
Range (Set I)
Range (Set II)
= 0
1
2
4
1
7
1
5
5
4
4
Range (Set III)
8.
Range (Set IV)
8.
3
7
1
4
10
10
(Type integers or decimals. Do not round.)
4
1
5
4
4
9.
1
5
5
4
e. Use the defining formula to compute the sample standard deviation of each data set.
s (Set l)
s (Set II)
%3D
Print
Done
s (Set III)
s (Set IV)
(Type integers or decimals. Round to one decimal place as needed.)
f. From your answers to parts (d) and (e), which measure of variation better distinguishes the spread in the four data sets: the range or the standard deviation? Explain your answer.
A. The standard deviation distinguishes spread better because it shows that the sets are structurally different, despite having similar ranges and means.
B. The standard deviation distinguishes spread better because it is resistant to outliers, and is therefore more robust than the range.
C. The range distinguishes spread better because it shows that having different standard deviations doesn't imply that the means must be different.
D. The range distinguishes spread better because it shows that the sets are structurally similar, because their extrema are equally spread out.
g. Are your answers from parts (c) and (e) consistent?
A. Yes, because there is a correlation between the range and the standard deviation of the data sets.
B. No, because it is not necessary that greater variation and greater standard deviation are correlated.
C. Yes, because the minimum and maximum standard deviations correspond to the data sets with the least and greatest variation, respectively.
D. No, because the minimum and maximum standard deviations do not correspond to the data sets with the least and greatest variation, respectively.
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