Respuesta :
The lower and upper bounds are 16.7 and 69.5 respectively.
So, the numbers are 30, 32, 37, 54, 67, 38, and 44.
In order to determine the lower bound and upper bound
Mean x' =Σ[tex]\frac{x}{n}[/tex] = 302/7 = 43.1429 = 43.1
Variance [tex]s^{2}[/tex] =Σ[tex]\frac{(x-x')^{2}}{n-1}[/tex] = 1048.86/(7-1) = 174.80952
Standard deviation = √174.80952 = 13.221555 = 13.2
Values that deviate more than two standard deviations from the mean are exceptional.
[tex]x -2s = 43.1 - 2*13.2 = 16.7[/tex] is the lower bound for uncommon values.
The upper bound that is exceptional is equal to
[tex]x + 2s = 43.1 + 2(13.2) = 69.5[/tex]
Therefore, 16.7 and 69.5 are the lower and upper bounds of given data
To learn more about Standard deviation click here:
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