Six different secondyear medical students at Bellevue Hospit

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?

132 138 130 144 125 132

Rangeequals=nothing

mmHg

Sample

varianceequals=nothing

mmHgsquared2

(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 one because this is the lowest standard deviation that can be achieved.

C.

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

D.

There is no way to tell what the standard deviation should be.

Solution

There are six different second-year medical students at Bellevue Hospital measured the blood pressure of the same person.

We have to find the range, variance, and standard deviation for the given sample data.

We make a table for this

xbar = x / n = 801 / 6 = 133.5 (Mean of the sample)

The formulae to compute range variance and standard deviation are,

Range = Largest observation - Smallest observation

Variance = (x - xbar )^2/(n-1)

Standard deviation = square root(variance)

n = number of observations = 6

Smallest observation = 125

Largest observation = 144

Range = 144 - 125 = 19 mmHg

Variance = 219.5 / (6-1)

= 219.5 / 5

= 43.9 mmHg²

Standard deviation = sqrt(43.9)

= 6.6257 mmHg

If the subject\'s blood pressure remains constant and the medical students correctly apply the same measurement technique that means blood pressure value for person gave the same reading to the all 6 students.

Then Variance = 0 implies that standard deviation = 0.

For example, suppose person\'s blood pressure is 132 then all student have get same reading i.e. 132 so mean of x is 132  (x-xbar)^2 is 0 thats why variance and standard deviation is also 0.

What should be the value of the standard deviation?

The option c) is correct.

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

This is an answer.