¶ … 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.
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
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