A= (11,12,13,9,15) b =(15,15,15,15,15) c=(3,3,12,21,21) d=(16,17,18,14,19) which data set has the largest standard deviation
Answers
Answer 15*15*15*15*15=759375 3*3*12*21*21=47628 16*17*18*14*19=1302336 11*12*13*9*15=231660 The answer is d
Given : Data Sets
a= (11,12,13,9,15)
b =(15,15,15,15,15)
c=(3,3,12,21,21)
d=(16,17,18,14,19)
To Find : which data set has the largest standard deviation
Solution:
One method is to find standard deviation of all the datas
S.D = √(xi - Mean)²/ n
But here data points are very less and can easily compare SD
a= (11,12,13,9,15) Range of Data = 15 - 9 = 6
b =(15,15,15,15,15) Range = 0
c=(3,3,12,21,21) Range = 21 - 3 = 18
d=(16,17,18,14,19) Range = 19 - 16 = 3
Just by seeing Range we can c=(3,3,12,21,21) will have largest standard deviation
However if we calculate using formula
a= (11,12,13,9,15) SD = 2
b =(15,15,15,15,15) SD = 0
c=(3,3,12,21,21) SD = 8.05
d=(16,17,18,14,19) SD = 1.72
c=(3,3,12,21,21) will have largest standard deviation
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