In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 11, 17, 9, 11, 10.
(a) Use the defining formula, the computation formula, or a
calculator to compute s. (Round your answer to one decimal
place.)
s =
(b) Multiply each data value by 6 to obtain the new data set 66,
102, 54, 66, 60. Compute s. (Round your answer to one
decimal place.)
s =
solution:-
given data set 11, 17, 9, 11, 10
(a) standard deviation = s = 3.1
explanation:-
standard deviation s = sqrt(∑(xi−X)^2/(n-1))
we have to find X = (11+17+9+11+10)/5 = 11.6
=> s = sqrt(∑(xi−X)^2/(n-1))
= sqrt(((11-11.6)^2 + (17-11.6)^2 + (9-11.6)^2 + (11-11.6)^2 + (10-11.6)^2)/(5-1))
= sqrt((0.36+29.16+6.76+0.36+2.56)/(4))
= 3.1
(b) given data 66, 102, 54, 66, 60
standard deviation s = 18.8
explanation:-
standard deviation s = sqrt(∑(xi−X)^2/(n-1))
we have to find xi = (66+102+54+66+60)/5 = 69.6
=> s = sqrt(∑(xi−X)^2/(n-1))
= sqrt(((69.6-66)^2 + (69.6-102)^2 + (54-69.6)^2 + (66-69.6)^2 + 60-69.9)^2)/(5-1))
= sqrt((12.96+1049.76+243.36+12.96+92.16)/4)
= 18.8
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