1.73) C-reactive protein (CRP) is a sunstance that can be measured in the blood.
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Question
1.73)
C-reactive protein (CRP) is a sunstance that can be measured in the blood. Values increase substantially within 6 hours of an infection and reach a peak within 24-48 hours. In adults, chronically high values have been linked to an increased risk of cardiovascular disease. In a study of apparently healthy children aged 6 to 60 months in Papua New Guinea, CRP was measured in 90 children . The units are milligrams per liter (mg/l). Here are the data from a random sample of 40 of these children:
(a)Find the five-number summary for these data.
(b) Make a boxplot
(c) Make a histogram
(d) Write a short summary of the major features of this distribution. Do you prefer the boxplot or the histogram for these data?
1.74)
Refer to the previous exercise. With strongly skewed distribution such as this, we frequently reduce the skewness by taking a log transformation. We have a bit of a problem here, however, because some of the data are recorded as 0.00, and the logarithm of zero is not defined. For this variable, the value 0.00 is recorded whenever the amount of CRP in the blood is below the level that the measuring instrument is capable of detecting. The usual procedure in this circcumstance is to add a small number to each observation before taking the logs. Transform these data by adding 1 to each observation and then taking the logarithm. Use the questions in the previous exercise as a guide to your analysis, and prepare a summary contrasting this analysis with the one that you performed in the previous exercise.
0.00 3.90 5.64 8.22 0.00 5.62 3.92 6.81 30.61 0.00 73.20 0.00 46.70 0.00 0.00 26.41 22.82 0.00 0.00 3.49 0.00 0.00 4.81 9.57 5.36 0.00 5.66 0.00 59.76 12.38 15.74 0.00 0.00 0.00 0.00 9.37 20.78 7.10 7.89 5.53Explanation / Answer
N=40
Median = 1/2(N+1) = 1/2*(41) = 20.5
1st Qunatile= 1/4(N+1) = 1/4(41)= 10.5,
3rd Qunatile= 3/4(41) = 30.75
a)Summary of data:
Min. : 0.000
1st Qu.: 0.000
Median : 5.085
Mean :10.032
3rd Qu.: 9.420
Max. :73.200
b) Box plot
c) Histogram
Plot normality and histogram:
d) On distributions around 40% data is zero. While referring box plot we can conclude there are few outliers present in the data. Histogram referring each set of a variable with a respective number. Distribution of data not following normality.
1.74)Log transformation while adding 1 to each variable.
Summary:
summary(t_log)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000 0.000 1.805 1.495 2.344 4.307
Box plot:
No outliers.
Histogram with normality:
Data has been transformed using Log. No outliers on data and data been following normality.
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