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?120 134 146 127 138 133

Answer 1

Answer:

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

Answer 2

Answer: 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