The STATA table below shows summary statistics from measurements of blood glucos
ID: 3203856 • Letter: T
Question
The STATA table below shows summary statistics from measurements of blood glucose levels from 18 diabetics learning how to correctly maintain their blood glucose levels. The blood glucose level should be kept between 90 - 130 mg/dl. The table give you nine percentiles including the median, the mean, the standard deviation, and the variance. It also contain the four lowest and the four highest observations. Answer the following questions:
a) Give a five number summary of the data!
b) Are there any outliers in this data set?
summ glucose detail Percentiles 1% 78 78 5% 10% 95 25% 112 50% 147.5 75% 172 90$ 271 95% 359 99% 359 glucose Smallest 78 95 96 103 Largest 200 255 271 359 Obs Sum of Wgt. Mean Std. Dev. Variance Question Completion Status 163.2778 70 65 559 4992.212Explanation / Answer
Answer)
a) Five number summary of the data is given as follows:
Minimum = 78
First Quartile = 112
Median = 147.5
Third Quartile = 172
Maximum = 359
b) Determining Outliers in a data set
To determine outliers we must consider the numbers that are 1.5*IQR or 10.5 beyond the quartiles.
IQR(Inter Quartile Range) = Third Quartile - First Quartile =172 - 112 = 60
First Quartile - 1.5*IQR = 112 - (1.5*60) = 22
Third Quartile + 1.5*IQR = 172 + (1.5*60) = 262
Since, there are data points which lie outside the interval (22 , 262) there are outliers in this data set.
c) By using Bowley's coefficient of skewness we can determine whether our data is skewed or not.
S = (Third Quartile + First Quartile - 2*Second Quartile) / (Third Quartile - First Quartile)
S = (172 + 112 - 2*147.5) / (172 - 112)
S = -11 / 60
S = -0.1834
Since, S = -0.1834 which is a negative value the distrbution is a negatively skewed distribution.
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