Question

Six different​ second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings​ (in mmHg) are listed below. Find the​ range, variance, and standard deviation for the given sample data. If the​ subject's blood pressure remains constant and the medical students correctly apply the same measurement​ technique, what should be the value of the standard​ deviation? 120 134 133 143 138 136 Rangeequals nothing mmHg Sample varianceequals nothing mmHgsquared ​(Round to the nearest tenth as​ needed.) Sample standard deviationequals nothing mmHg​ (Round to the nearest tenth as​ needed.) What should be the value of the standard​ deviation? A. ​Ideally, the standard deviation would be one because all the measurements should be the same. B. ​Ideally, the standard deviation would be zero because all the measurements should be the same. C. ​Ideally, the standard deviation would be one because this is the lowest standard deviation that can be achieved. D. There is no way to tell what the standard deviation should be.

Answer 1

(a)
Range = Maximum - Minimum = 143 - 120 = 23.

So,

Range = 23 mmHg

(b)

n = 6

Sample mean () is calculated as follows:

x	(x - )	(x - )2
120	- 14	196
134	0	0
133	- 1	1
143	9	81
138	4	16
136	2	4
Total =		298

Sample Variance (s²) is given by:

So,

Sample Variance = 59.6 mmHg²

(c)

Sample Standard Deviation (s) is given by:

So,

Sample Standard Deviation = 7.7 mmHg

(d)

Correct option:

B.   Ideally, the standard deviation would be zero because all the measurements should be the same.