Question

the following are the ratings of men by women in an experiment involving speed dating. use the given data to construct a boxplot and identify the 5 - number summary. 2.0 2.0 3.0 3.0 3.5 3.5 4.0 4.0 4.0 4.0 4.0 5.0 5.0 6.0 6.0 6.0 7.0 7.0 8.0 8.0 the 5 - number summary is □, □□□ and □. (use ascending order. type integers or decimals. do not round.)

Explanation:

Step1: Find the minimum value

The minimum value is the smallest number in the data set. Looking at the data \(2.0, 2.0, 3.0, 3.0, 3.5, 3.5, 4.0, 4.0, 4.0, 4.0, 4.0, 5.0, 5.0, 6.0, 6.0, 6.0, 7.0, 7.0, 8.0, 8.0\), the minimum \(Q_0 = 2.0\).

Step2: Find the first - quartile (\(Q_1\))

The formula for the position of \(Q_1\) is \(i=\frac{n + 1}{4}\), where \(n = 20\) (the number of data points). So \(i=\frac{20+1}{4}=5.25\).
The first - quartile \(Q_1\) is calculated as \(Q_1=x_5+(x_6 - x_5)\times0.25\). Here \(x_5 = 3.5\) and \(x_6 = 3.5\), so \(Q_1=3.5+(3.5 - 3.5)\times0.25=3.5\).

Step3: Find the median (\(Q_2\))

The formula for the position of the median is \(i=\frac{n + 1}{2}\). For \(n = 20\), \(i=\frac{20 + 1}{2}=10.5\).
The median \(Q_2=x_{10}+(x_{11}-x_{10})\times0.5\). Here \(x_{10}=4.0\) and \(x_{11}=4.0\), so \(Q_2=4.0+(4.0 - 4.0)\times0.5 = 4.0\).

Step4: Find the third - quartile (\(Q_3\))

The formula for the position of \(Q_3\) is \(i=\frac{3(n + 1)}{4}\). For \(n = 20\), \(i=\frac{3(20 + 1)}{4}=15.75\).
The third - quartile \(Q_3=x_{15}+(x_{16}-x_{15})\times0.75\). Here \(x_{15}=6.0\) and \(x_{16}=6.0\), so \(Q_3=6.0+(6.0 - 6.0)\times0.75=6.0\).

Step5: Find the maximum value

The maximum value is the largest number in the data set. So the maximum \(Q_4 = 8.0\).

Answer:

\(2.0\), \(3.5\), \(4.0\), \(6.0\), \(8.0\)