Question

Which group has the smaller standard deviation?

Select one:

a. Group A: 1,2,3,10,20,25,30,40.

b. Group B: 1,5,10,15,20,25,30.

c. Group C: 20,21,22,23,24,25,26.

d. Group D: 20,40,50,60,80,100,110.

Answer 1

Solution:

Standard deviation can be calculated as

Sd = sqrt(summation(Xi-Xbar)^2)/n)

Mean of group1=(1+2+3+10+20+25+30+40)/8 = 131/8= 16.375

SD= sqrt((1-16.375)^2 +(2-16.375)^2+(3-16.375)^2+(10-16.375)^2+(20-16.375)^2+(25-16.375)^2+(30-16.375)^2+(40-16.375)^2)/8))= sqrt(186.73) = 13.665

Mean for Group 2 = 15.14

Standard deviation for Group2= 9.79

Mean for Group 3= 23

Standard deviation for Group3= 2

Mean for Group 4= 65.71

Standard deviation for group 4 = 30.17

So we can see that group C has smaller standard devaition.