Question

the following data represent the dividend yields (in percent) of a random sample of 28 publicly traded stocks. complete parts (a) to (c).
(a) compute the five - number summary.
the five - number summary is 0, 0.19, 0.83, 2.43, 3.59
(round to two decimal places as needed. use ascending order.)
(b) draw a boxplot of the data.

Explanation:

Step1: Arrange the data in ascending order

0, 0, 0, 0.04, 0.07, 0.15, 0.22, 0.33, 0.35, 0.42, 0.45, 0.53, 0.67, 0.99, 1.09, 1.53, 1.81, 1.85, 1.96, 2.21, 2.64, 2.68, 2.8, 2.87, 2.88, 3.13, 3.59

Step2: Find the minimum value

The minimum value is the first value in the ordered list.
$0$

Step3: Find the first quartile ($Q_1$)

For $n = 28$ (even), the position of $Q_1$ is $\frac{n + 1}{4}=\frac{28+1}{4}=7.25$.
$Q_1=0.22+(0.33 - 0.22)\times0.25=0.25$

Step4: Find the median ($Q_2$)

The position of the median for $n = 28$ (even) is $\frac{n}{2}=14$ and $\frac{n}{2}+1 = 15$.
$Q_2=\frac{0.99 + 1.09}{2}=1.04$

Step5: Find the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(28 + 1)}{4}=21.75$.
$Q_3=2.64+(2.68 - 2.64)\times0.75=2.67$

Step6: Find the maximum value

The maximum value is the last value in the ordered list.
$3.59$

Answer:

The five - number summary is $0$, $0.25$, $1.04$, $2.67$, $3.59$