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 □,□,□,□,□
(round to two decimal places as needed. use ascending order.)

Explanation:

Step1: Sort the data

First, we sort the given data in ascending order:
\(0,0,0,0.07,0.08,0.08,0.12,0.15,0.18,0.22,0.34,0.42,0.45,0.58,0.97,1.07,1.79,1.81,2.17,2.24,2.26,2.56,2.72,2.84,2.93,2.94,3.62,3\)

Step2: Find the minimum value

The minimum value (\(Q_0\)) is the first value in the sorted list. So, \(Q_0 = 0\)

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

Since \(n = 28\), the position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{28+1}{4}=7.25\)
\(Q_1=0.12+(0.15 - 0.12)\times0.25=0.1275\approx0.13\)

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

The position of the median for \(n = 28\) (even number of data points) is \(\frac{n}{2}=14\) and \(\frac{n}{2}+1 = 15\)
\(Q_2=\frac{0.58 + 0.97}{2}=0.775\approx0.78\)

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

The position of \(Q_3\) is \(\frac{3(n + 1)}{4}=\frac{3\times(28 + 1)}{4}=21.75\)
\(Q_3=2.26+(2.56 - 2.26)\times0.75=2.26+0.225 = 2.485\approx2.49\)

Step6: Find the maximum value

The maximum value (\(Q_4\)) is the last value in the sorted list. So, \(Q_4 = 3.62\)

Answer:

\(0,0.13,0.78,2.49,3.62\)