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 data in ascending order:
\(0,0,0,0,0.04,0.07,0.15,0.22,0.33,0.35,0.42,0.45,0.53,0.67,0.99,1.09,1.53,1.81,1.85,1.96,2.21,2.64,2.68,2.8,2.87,2.88,3.13,3.59\)

Step2: Find the minimum value

The minimum value (\(Q_0\)) 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 \(\frac{n + 1}{4}=\frac{28+1}{4}=7.25\)
\(Q_1=0.15+(0.22 - 0.15)\times0.25=0.15 + 0.0175=0.17\)

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

The position of the median is \(\frac{n+1}{2}=\frac{28 + 1}{2}=14.5\)
\(Q_2=\frac{0.67+0.99}{2}=0.83\)

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

The position of \(Q_3\) is \(\frac{3(n + 1)}{4}=\frac{3\times(28+1)}{4}=21.75\)
\(Q_3=2.21+(2.64 - 2.21)\times0.75=2.21+0.3225 = 2.53\)

Step6: Find the maximum value (\(Q_4\))

The maximum value (\(Q_4\)) is the last value in the sorted list. So, \(Q_4=3.59\)

Answer:

\(0,0.17,0.83,2.53,3.59\)