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 0.598, 0.599, 0.600, 0.604, 0.611
(use ascending order.)
choose the correct boxplot of the data below.
a.
b.
c.

Explanation:

Step1: Analyze the five - number summary

The five - number summary consists of the minimum value ($0.598$), the first quartile ($Q_1 = 0.599$), the median ($Q_2=0.600$), the third quartile ($Q_3 = 0.604$), and the maximum value ($0.611$).

Step2: Determine the shape of the distribution

In a boxplot, if the median is approximately in the middle of the box (i.e., the distance from $Q_1$ to the median is similar to the distance from the median to $Q_3$) and the whiskers are of similar lengths relative to the box, the distribution is approximately symmetric. Here, $Q_2 - Q_1=0.600 - 0.599 = 0.001$ and $Q_3 - Q_2=0.604 - 0.600=0.004$ (relatively close), and the whiskers do not show extreme skewness (the minimum is $0.598$ and the maximum is $0.611$, $0.600 - 0.598 = 0.002$ and $0.611 - 0.600=0.011$, but overall the box and median position suggest a near - symmetric shape).

Answer:

The distribution is approximately symmetric.