Question

the following data represent the weight (in grams) of a random sample of 13 medicine tablets. find the five - number summary, and construct a boxplot for the data. comment on the shape of the distribution.
0.599 0.601 0.598 0.606
0.600 0.604 0.599 0.602
0.611 0.598 0.600 0.604
0.600
the five - number summary is □, □, □, □, □.
(use ascending order.)

Explanation:

Step1: Sort the data

First, sort the data in ascending order: \(0.598, 0.598, 0.599, 0.599, 0.600, 0.600, 0.600, 0.601, 0.602, 0.604, 0.604, 0.606, 0.611\)

Step2: Find the minimum

The minimum value is the first value in the sorted list: \(0.598\)

Step3: Find the first quartile (\(Q_1\))

Since \(n = 13\), \(n/4=3.25\). \(Q_1\) is the \(4^{th}\) value. \(Q_1 = 0.599\)

Step4: Find the median (\(Q_2\))

Since \(n = 13\), the median is the \((n + 1)/2=7^{th}\) value. \(Q_2=0.600\)

Step5: Find the third quartile (\(Q_3\))

Since \(3n/4 = 9.75\), \(Q_3\) is the \(10^{th}\) value. \(Q_3=0.604\)

Step6: Find the maximum

The maximum value is the last value in the sorted list: \(0.611\)

Answer:

The five - number summary is \(0.598, 0.599, 0.600, 0.604, 0.611\)