Which data set has the highest standard deviation (without doing calculations)?

a) 1,2,3,4

b) 1,1,1,4

c) 1,2,2,4

d) 4,4,4,4

B)1,1,1,4

Step-by-step explanation:

A.1,2,3,4

Mean=

x      

1       -1.5                                2.25

2       -0.5                              0.25

3         0.5                              0.25  

4          1.5                               2.25

B.

Mean=

0.5625

0.5625

0.5625

5.0625

C.

Mean=

1.5625

0.0625

0.0625

3.0625

D.

0

0

0

0

We know that

S.D is directly proportional to  .

When is highest  then the S.D is also highest.

We can see that  the value of   is highest  in option B.

Therefore, S.D of the date set of  option B is highest.