Respuesta :
Given that mean of quiz scores = 6.4 and standard deviation = 0.7
And we need to use Chebyshev's theorem to find the range in which 88.9% of data will reside.
Chebyshev's theorem states that "Specifically, no more than [tex]\frac{1}{k^{2} }[/tex] of the distribution's values can be more than k standard deviations away from the mean".
That is [tex]1-\frac{1}{k^{2} } = 0.889[/tex]
[tex]\frac{1}{k^{2} } = 1-0.889 = 0.111[/tex]
[tex]k^{2} = \frac{1}{0.111}[/tex]
k = 3
So, we want the range of values within 3 standard deviations of mean.
Hence range is [mean -3*standard deviation, mean +3*standard deviation]
= [6.4 - 3*0.7 , 6.4+3*0.7]
= [6.4 - 2.1 , 6.4+2.1] = [4.3,8.5]
Given that mean of quiz scores = 6.4 and standard deviation= 0.7
And we need to use Chebyshev's theorem to find the range in which 88.9% of data will reside.
Chebyshev's theorem states that "Specifically, no more than of the distribution's values can be more than k standard deviations away from the mean".
That is 1-1/k2 = 0.889.
1/k2 = 1-0.889 = 0.111.
k2=0.111.
K= 3.
So, we want the range of values within 3 standard deviations of mean.
Hence range is mean -3 x standard deviation, mean +3x standard deviation
= [6.4 - 3x 0.7 , 6.4+3 x 0.7]
= [6.4 - 2.1 , 6.4+2.1] = [4.3,8.5]
Statistics
Statistics is the discipline that concerns the collection, organization, analysis, interpretation and presentation of data.
Read more about statistics here:
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