O Compute a 75% Chebyshev interval around the sample mean.
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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100%
![(b) Compute a 75% Chebyshev interval around the sample mean.
Recall that Chebyshev's Theorem states that for any set of data and for any constant k greater than 1,
the
1
proportion of the data that must lie within k standard deviations on either side of the mean is at least 1
1
of data must fall between
k?
Therefore, for sample data with mean x and standard deviation s, at least 1
X -
ks and x + ks.
When k =
2, we have the following.
1
1
1
k2
1
22
1
= 1
or
4
Therefore, for any set of data, at least 75% of the data must fall between x
2s and x +
or, in other words, within
standard deviations of the mean.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd1a2ee6-03ad-4656-9c76-894ab5655db1%2F2acadaea-6c1d-4c81-8379-a3103131ac3a%2Fgny6wfj_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Compute a 75% Chebyshev interval around the sample mean.
Recall that Chebyshev's Theorem states that for any set of data and for any constant k greater than 1,
the
1
proportion of the data that must lie within k standard deviations on either side of the mean is at least 1
1
of data must fall between
k?
Therefore, for sample data with mean x and standard deviation s, at least 1
X -
ks and x + ks.
When k =
2, we have the following.
1
1
1
k2
1
22
1
= 1
or
4
Therefore, for any set of data, at least 75% of the data must fall between x
2s and x +
or, in other words, within
standard deviations of the mean.
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