¶ … Probability
Summarizing Data and Probability Variance
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.
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…
References
Joseph, L., Reinhold, C. (2002). Introduction to Probability Theory and Sampling Distributions. Fundamentals of Clinical Research for Radiologists.
Waller, D. L. (2008). Statistics for Business. United Kingdom: Butterworth-Heinemann.
An example of a business situation where the probability distribution may be utilized is a scenario where a manager attempts to predict employee retention. The statistical test would be a binary logistic regression analysis. The probability distribution is paramount to this example because it utilizes the dichotomous dependent variable of Yes/No (employee stays/employee quits). Independent variables that may be used to predict employee retention include education level, length of employment,
Probability Probabilities according to Becker and Parker (2011) are used in both simulations and real life scenarios to help in the estimation of the occurrence of events. In the words of Gravetter and Wallnau (2008), "for a situation in which several different outcomes are possible, the probability for any specific outcome is defined as a fraction or a proportion of all the possible outcomes." In that regard, chance and randomness are
Probability Concepts & Applications (1) Describe the rationale for utilizing probability concepts. Is there more than one type of probability? If so, describe the different types of probability. One uses probability mathematics in order to assess the probability of a particular occurrence or the results of a particular action; For instance, whether or not one should go into a certain market or invest in a certain product -- what are the chances
Probability provides a measurable and quantifiable indication of how likely a particular outcome is for an event or experiment. It is expressed as a numeric value between zero and one (inclusive), where an impossible event has a probability of zero and a certain event has a probability of one. Probability is conventionally written using the symbol P, and may be expressed as a percentage by multiplying P. By 100. The problem
The use of databases as the system of record is a common step across all data mining definitions and is critically important in creating a standardized set of query commands and data models for use. To the extent a system of record in a data mining application is stable and scalable is the extent to which a data mining application will be able to deliver the critical relationship data,
Introduction The business taken into account for the analysis is Google, Inc. The primary data being collected is on Google and on different mobile applications to evaluate the validity of whether the latter are becoming more significant and popular compared to Google. In this case, the independent variable is percentage of internet usage on Google for every period. Basically, the metric taken into consideration is the percentage of time spent on