a. What is the 25th percentile of HDL in patients recelving the placebo? b What is median HDL. in patients receiving the new drug? c Are there any outliers in HDLin patients recein ng the new drug? Justify.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
a.
First quartile:
First quartile is the median of all the observations that are left to the ‘location of overall median’. It is the 25th percentile which determines the 25% of the data values lie below the first quartile. In the boxplot, the bottom line (towards left) of the box represents the first quartile.
From the boxplot of HDL cholesterol, the first quartile value for patients receiving placebo corresponds to the bottom line (towards left) of the box. The bottom line of the boxplot for placebo corresponds to the value 35. The first quartile or the 25th percentile is 35.
Thus, the 25th percentile of HDL patients receiving placebo is 35.
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