Question

10 samples of 4140 steel (as received) were tensile tested from a population of 1000+ and the yield strengths had a frequency distribution as shown: Yield Strength (ksi Frequency 72 69 65 64 58 What is the approximate standard deviation of the yield strengths of the which the samples were taken? a) 4.43 b) 4.67 c) 4.76 d) 5.32

No excel, show work please.

Answer 1

Occurance(X)	Frequency(f)	Freq*X	(X-mean)	(X-mean)2	f*(X-mean)2
72	1	72	6.7	44.89	44.89
69	3	207	3.7	13.69	41.07
65	2	130	-0.3	0.09	0.18
64	2	128	-1.3	1.69	3.38
58	2	116	-7.3	53.29	106.58
Total ->	10	653	-	-	196.1

Mean = 65.3

Standard Deviation = 4.668

Standard Deviation = 4.67

Answer: Option (b)