A sample of six resistors yielded the following resistances

A sample of six resistors yielded the following resistances (ohms): x_1 = 47, x_2 = 37, x_3 = 50, x_4 = 41, x_5 = 34, and x_6 = 44 Compute the sample variance and sample standard deviation. Subtract 34 from each of the original resistance measurements and compute s^2 and s. Compare your results with those obtained in part (a). If the resistances were 470, 370, 500, 410, 340, and 440 ohms, could you use the results of previous parts of this problem to find s^2 and s ? Round your answers to 2 decimal places. Shifting the data from the sample by a constant amount on the sample variance or standard deviation.

Solution

When each entry is multiplied by 10,

E(10x) = Mean = 10(8.16667) = 81.6667=81.67

Var(10x) =100 var x = 3656.667 = 3656.67

Std dev (10x) = 60.47038 = 60.47

a)	x	47	37	50	41	34	44	42.16667	6.047038	36.56667
b)	X-34	13	3	16	7	0	10	8.166667	6.047038	36.56667
	Thus by reducing 34 from each entry, mean reduces by 34 but std dev and variance remain the same.
c)	10x