Question

"An engineer is working to determine the pullout force in in-lbs of a pin inside of an electrical connector. Eight samples are tested with the following results: 12.6, 12.9, 13.4, 12.3, 13.6, 13.5, 12.6, 13.1. For this data set, what is the standard deviation?"

Answer 1

For the given data set 12.6, 12.9, 13.4, 12.3, 13.6, 13.5, 12.6, 13.1. to find the standard deviation we need to find the mean first as:

Mean = (12.6 + 12.9 + 13.4 + 12.3 + 13.6 + 13.5 + 12.6 + 13.1)/8
= 104/8
Mean, = 13

The sample standard deviation is calculated as:

σ = √(1/8 - 1) x ((12.6 - 13)² + ( 12.9 - 13)² + ( 13.4 - 13)² + ( 12.3 - 13)² + ( 13.6 - 13)² + ( 13.5 - 13)² + ( 12.6 - 13)² + ( 13.1 - 13)²)
= √(1/7) x ((-0.4)² + (-0.1)² + (0.4)² + (-0.7)² + (0.6)² + (0.5)² + (-0.4)² + (0.1)²)
= √(0.1429) x ((0.16) + (0.0099999999999999) + (0.16) + (0.49) + (0.36) + (0.25) + (0.16) + (0.0099999999999999))
= √(0.1429) x (1.6)
= √(0.22864)
= 0.4781