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 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 minimum value

The minimum value is the first value in the ordered list, which is \(0\).

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

Since \(n = 28\), the position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{28+1}{4}=7.25\).
\(Q_1=0.22+(0.33 - 0.22)\times0.25=0.22 + 0.0275=0.25\) (rounded to two decimal places)

Step4: Find median (\(Q_2\))

The position of the median is \(\frac{n + 1}{2}=\frac{28+1}{2}=14.5\).
\(Q_2=\frac{0.99+1.09}{2}=1.04\)

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

The position of \(Q_3\) is \(3\times\frac{n + 1}{4}=3\times\frac{28 + 1}{4}=21.75\).
\(Q_3=2.64+(2.68 - 2.64)\times0.75=2.64+0.03=2.67\)

Step6: Find maximum value

The maximum value is the last value in the ordered list, which is \(3.59\)

Answer:

The five - number summary is \(0\), \(0.25\), \(1.04\), \(2.67\), \(3.59\)