Question

Would you please demonstrate to me how to create dataset A and dataset B,
where dataset A has a larger range but smaller standard deviation than
dataset B. Then the reverse where data set A has a smaller range and larger standard deviation than data set B.

Answer 1

Case 1:

Data set A: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Sample size, n =10

Range(A) =maximum value - minimum value =10 - 1 =9

Mean, = =5.5

Standard deviation, S_A = =3.028

Data set B: 2, 2, 4, 4, 8, 8, 9, 10, 10, 10

Sample size, n =10

Range(B) =maximum value - minimum value =10 - 2 =8

Mean, = =6.7

Standard deviation, S_B = =3.335

Conclusion:

Range(A): 9 > Range(B): 8

S_A: 3.028 < S_B: 3.335

Thus, data set A has a larger range but smaller standard deviation than data set B.

Case 2:

We can take the same data sets above but their names have to be reversed - data set A as data set B and data set B as data set A.

However, let us take other data sets.

Data set A: 12, 13, 13, 14, 18, 28, 28, 28, 30, 30

Range(A) =maximum value - minimum value =30 - 12 =18

Mean, = =21.4

Standard deviation, S_A = =7.99

Data set B: 10, 12, 15, 19, 22, 26, 26, 28, 30, 32

Range(B) =maximum value - minimum value =32 - 10 =22

Mean, = =22

Standard deviation, S_B = =7.70

Conclusion:

Range(A): 18 < Range(B): 22

S_A: 7.99 > S_B: 7.70

Thus, data set A has a smaller range but larger standard deviation than data set B.