Question

In which of the following sets of values is the mean equal to the standard deviation? Group of answer choices 2, 4, 6, 8, 9

4, 7, 8, 8, 12

0, 2, 4, 6, 13

2, 4, 5, 9, 11

Answer 1

Solution:
we will calculate Mean and standard deviation of all groups as follows:
Mean = Xi/n
Standard deviation = sqrt(((Xi-mean)^2/(n-1)
Group1 : 2,4,6,8,9
Mean = (2+4+6+8+9)/5 = 29/5 = 5.8
Standard deviation = sqrt((2-5.8)^2 + (4-5.8)^2 + (6-5.8)^2 + (8-5.8)^2 +(9-5.8)^2)/4) = 2.86
Group 2: 4,7,8,8,12
Mean = (4+7+8+8+12)/5 = 7.8
Standard deviation = sqrt((4-7.8)^2 + (7-7.8)^2 + (8-7.8)^2 + (8-7.8)^2 +(12-7.8)^2)/4) = 2.86
Group3: 0,2,4,6,13
Mean = (0+2+4+6+13)/5 = 5
Standard deviation = sqrt((0-5)^2 + (2-5)^2 + (4-5)^2 + (6-5)^2 +(12-5)^2)/4) = 5
Group4: 2,4,5,9,11
Mean = (2+4+5+9+11)/5 = 6.2
Standard deviation = sqrt((2-6.2)^2 + (4-6.2)^2 + (5-6.2)^2 +(9-6.2)^2 +(11-6.2)^2)/4) = 3.70

From the above solutions we can say that Set 3 has the same mean(5) and standard deviation(5).