Analysis of Data and Probability Case Study

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Probability

Summarizing Data and Probability

Blood Pressure Data

Patient ID

Systolic

Diastolic

1st Patient

2nd Patient

3rd Patient

4th Patient

5th Patient

6th Patient

7th Patient

8th Patient

9th Patient

Diastolic Blood Pressure Measurements

Mean

Mean is also referred to as average. This is obtained by adding up a set of tallies and thereafter dividing the resulting summation by the number of tallies. The general formula for obtaining mean is as follows:

Mean of the systolic blood pressure measurements

Mean of the diastolic blood pressure measurements

Median

The median is the middle value of an ordered set or list of numbers.

Median of the systolic blood pressure measurements

Ordered set is as follows:

90, 110, 120, 120, 130, 130, 150, 150, 160

Therefore, the median is 130

Median of the diastolic blood pressure measurements

Ordered set is as follows

40, 60, 60, 70, 80, 80, 90, 90, 110

Therefore, the median is 80

1. Standard Deviation

The standard deviation is calculated using the following formula:

i. Standard deviation for systolic blood pressure measurements

Patient ID

Systolic

x - µ

(x -µ )2

1st Patient

31.

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11111

2nd Patient

21.11111

3rd Patient

-18.8889

4th Patient

-8.88889

79.01235

5th Patient

1.

1.234568

6th Patient

21.11111

7th Patient

1.

1.234568

8th Patient

-8.88889

79.01235

9th Patient

90

-38.8889

Summation

1,160

3,889

Mean

= 3,889 / (9-1)

= 3,889 / 8

= 486.125

Standard deviation = ?486.125

= 22.05

ii. Standard deviation for diastolic blood pressure measurements

Patient ID

Diastolic

x - µ

(x -µ )2

1st Patient

34.44444

2nd Patient

90

14.44444

3rd Patient

60

-15.5556

4th Patient

80

4.

19.75309

5th Patient

70

-5.55556

30.8642

6th Patient

90

14.44444

7th Patient

80

4.

19.75309

8th Patient

60

-15.5556

9th Patient

40

-35.5556

Summation

Mean

75.55556

= 3,422.22 / (9-1)

= 3,422.22 / 8

= 427.7775

Standard deviation = ?427.7775

= 20.68

1. Variance

The variance is obtained by squaring the standard deviation. Therefore, the variance is obtained as (std. dev) 2.

i. Variance.....

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