O Compute a 75% Chebyshev interval around the sample mean.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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(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.
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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