Analysis of Data and Probability

¶ … 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

31.11111

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 for diastolic blood pressure measurements

20.682 = 427.66

ii. Variance for systolic blood pressure measurements

22.052 = 486.20

Histogram and box plot for systolic blood pressure

0. Histogram

Bin

Frequency

85

0

1

1

4

0

3

More

0

Histogram and box plot for diastolic blood pressure

Bin

Frequency

40

1

60

2

80

3

2

1

More

0

Systolic

Diastolic

Min

90

40

Q1

60

Median

80

Q3

90

Max

Problem 2

The inference from the statistics undertaken above show that patients have a higher systolic blood pressure measurements compared to diastolic measurements on average. This can be perceived from the means of the two sets of data. From the histograms that have been plotted, one can infer that the data follows a normal distribution. This is because the shape of the histogram offers the resemblance of a bell-shaped curve, which indicates that the data is normal. Both the systolic and diastolic data measurements are somewhat of a bell-shaped curve. However, data for diastolic blood pressure measurements have a more normal distribution (Waller, 2008).

Part 2

Problem 3

Specific ways in which probability is used in clinical research

One specific way in which probability is used in clinical research on a daily basis is in making medical decisions centered on results from different radiologic diagnostic implements. In radiologic research, one often requires to make conclusions regarding the comparative performance of one analytical tool matched with a different one for the uncovering of a certain disorder of interest. Such clinical research relies, for most part, on probability theory and its applications (Joseph and Reinhold, 2002). The other specific way is in diagnosis, where the clinical researchers are vested in computing the probability that the condition of interest is present because of results of a certain clinical test. This probability hinges on how profound and precise that test is in diagnosing the condition and on the contextual rate of the condition in the population (Joseph and Reinhold, 2002). For clinical research trials to be successful, probability has to be applied in making decisions for the circumstances and situations that are pertinent to the research (Joseph and Reinhold, 2002).