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?120 134 146 127 138 133

range= 26, variance= 80 and standard deviation= 8.94

Step-by-step explanation:

Range = highest - lowest

Range = 146 - 120

Range= 26

Let m be mean

M=mean=sum/n

Mean=(120+134+146+127+138+133) / 6

M=798/6

M=133

The standard deviation sample formula:

S.D = sqrt( Summation of |x-m|^2 / n-1)

Let start finding:

|x-m|^2

For 1st: |120-133|^2=169

For 2nd: |134-133|^2=1

For 3rd: |146-133|^2=169

For 4th: |127-133|^2=36

For 5th: |138-133|^2=25

For 6th: |133-133|^2=0

Summation of |x-m|^2 = 400

The standard deviation formula is :

S.D = sqrt( Summation of |x-m|^2 / n-1)

S.D= sqrt(400 / 5)

S.D=sqrt(80)

S.D= 8.94

Variance = (Summation of |x-m|^2 / n-1)

Variance= 400/5

Variance= 80

Part A.

Range= 26

Variance= 66.67

Standard deviation= 8.165

Part B.

If the blood pressure remains constant and all the six medical student gets the same result from the blood pressure, The standard deviation will be; The value which is the same minus the average value.

Step-by-step explanation:

The values of their result are 120, 134, 146, 127, 138, and 133

FIND RANGE:

The range is the highest value minus the lowest value

146 is the highest value

120 is the lowest value

146-120= 26

FIND VARIANCE :

Variance is the mean value of the sum of the square of the difference between each value and the mean.

Variance= ∑[( x- X)]/n

Step 1: find the mean

(120+134+146+127+138+133)/6

= 133

Step2: square the difference between each value and the mean.

(120-133)^2=169

(134-133)^2=1

(146-133)^2=169

(127-133)^2=36

(138-133)^2=25

(133-133)^2=0

Step 3: find the average of the values in step 2.

(169+1+169+36+25+0)/6

= 400/6 = 66.67

FIND THE STANDARD DEVIATION:

The standard deviation is the square root of the variance.

√66.67= 8.165.

IF THE VALUES OF THEIR RESULT ARE THE SAME, STANDARD DEVIATION WILL BE

x - X

Where;

x is the value of the number which is the same for the six student

X is the mean value of the number which is the same for the six student

the graph top, left is y = 4x

the first one, all those points on the line just make a strait line.