Measurements:
37.3055 g 37.4005 g 37.4673 g 37.3520 g 37.5109 g 37.3970 g 37.4819 g 37.2700 g 37.3763 g
a) The first step to find the standard deviation is to find the mean of these measurements. We have to add all the measurements and then divide them by 9.
mean = (37.3055 g + 37.4005 g + 37.4673 g + 37.3520 g + 37.5109 g + 37.3970 g + 37.4819 g + 37.2700 g + 37.3763 g) / 9
mean = 37.3957 g
b) Then for each number we substract the mean:
37.3055 g - 37.3957 g = - 0.0902
37.4005 g - 37.3957 g = 0.0048
37.4673 g - 37.3957 g = 0.0716
37.3520 g - 37.3957 g = -0.0437
37.5109 g - 37.3957 g = 0.1152
37.3970 g - 37.3957 g = 0.0013
37.4819 g- 37.3957 g = 0.0862
37.2700 g - 37.3957 g = -0.1257
37.3763 g - 37.3957 g = -0.0194
c) Now we have to square those results:
(0.0902 g)² = 0.00813604
(0.0048 g)² = 0.00002304
(0.0716 g)² = 0.00512656
(-0.0437 g)² = 0.00190969
(0.1152 g)² = 0.01327104
(0.0013 g)² = 0.00000169
(0.0862 g)² = 0.00743044
(-0.1257 g)² = 0.01580049
(-0.0194 g)² = 0.00037636
d) Now we have to add all those values:
0.00813604 + 0.00002304 + 0.00512656 + 0.00190969 + 0.01327104 + 0.00000169 + 0.00743044 + 0.01580049 + 0.00037636 = 0.05207535
e) Now we divide that result by the total number of values (they are nine measurements):
0.05207535/9 =