Exercise Quiz 1

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Question 1 of 1

Two different brands of tablets with the same active compound are compared with respect to their solubility. For each of the two brands 10 tablets were investigated. For each tablet, percent solubility is measured after the tablet have been kept in 1000 ml de-ionized water for a while. One measurement failed, so the following values for percent solubility were found:

Brand F	45	47	48	49	49	50	52	52	53	54
Brand G	48	48	49	49	52	54	54	55	55

What are the following five numbers for Brand G: $0\%$-percentile, lower quartile $Q_1$, median, upper quartile $Q_3$, and $100\%$-percentile?

$0$, $ 49.5$, $51.56$, $ 55$, $ 100$

$48$, $ 49$, $52$, $ 54$, $ 55$

With $n=9$ we could use the quantile definition procedure a number of times. However, since the median of these 9 numbers is the middle number, that is 52, the only possible correct answer is 2: $48$, $ 49$, $52$, $ 54$, $ 55$. (And we don’t have to think about how to define the 0\% and 100\% percentiles - which simply are defined as the minimum and maximum values)

In Python:


brand_G = np.array([48, 48, 49, 49, 52, 54, 54, 55, 55])
   np.quantile(brand_G,[0,0.25,0.5,0.75,1],method = 'averaged_inverted_cdf')
array([48., 49., 52., 54., 55.])

$0$, $ 25$, $50$, $ 75$, $ 100$

$51.56-2\cdot 3.05$, $ 51.56-3.05$, $51.56$, $ 51.56+3.05$, $51.56+2\cdot 3.05$

$51.56-2\cdot 3.05/9$, $ 51.56-3.05/9$, $51.56$, $ 51.56+3.05/9$, $51.56+2\cdot 3.05/9$