Question

1. fill in the values below and use them to create a box and whiskers plot for the following set of data. 4,5,7,8,10,10,11,13,13,14,15,15 min: 4 q1: _ med: _ q3: _ max: 15 3. fill in the values below and use them to create a box and whiskers plot for the following set of data. 1,2,4,5,6,7,9,10,11,11,12,13,13 min: 1 q1: _ med: _ q3: _ max: 13

Explanation:

Step1: Find Min and Max

The minimum (Min) is the smallest value in the data set. For the first data set \(4,5,7,8,10,10,11,13,13,14,15,15\), \(Min = 4\). For the second data set \(1,2,4,5,6,7,9,10,11,11,12,13,13\), \(Min=1\). The maximum (Max) is the largest value. For the first data set, \(Max = 15\). For the second data set, \(Max = 13\).

Step2: Find the median (Med)

The median is the middle - value. For a data set with \(n\) values, if \(n\) is even, \(Med=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}\); if \(n\) is odd, \(Med = x_{\frac{n + 1}{2}}\) (where \(x_i\) is the \(i\) - th ordered value).

• First data set: \(n = 12\) (even). \(x_6=10\), \(x_7 = 11\). \(Med=\frac{10 + 11}{2}=10.5\).
• Second data set: \(n = 13\) (odd). \(\frac{n + 1}{2}=7\). \(Med=x_7 = 9\).

Step3: Find \(Q_1\) and \(Q_3\)

\(Q_1\) is the median of the lower half of the data, and \(Q_3\) is the median of the upper half of the data.

• First data set:
• Lower half: \(4,5,7,8,10,10\). \(n = 6\) (even). \(Q_1=\frac{7+8}{2}=7.5\).
• Upper half: \(11,13,13,14,15,15\). \(n = 6\) (even). \(Q_3=\frac{13 + 14}{2}=13.5\).
• Second data set:
• Lower half: \(1,2,4,5,6,7\). \(n = 6\) (even). \(Q_1=\frac{4+5}{2}=4.5\).
• Upper half: \(11,11,12,13,13\). \(n = 5\) (odd). \(\frac{n + 1}{2}=3\). \(Q_3=12\).

Answer:

• For the data set \(4,5,7,8,10,10,11,13,13,14,15,15\): \(Min = 4\), \(Q_1=7.5\), \(Med = 10.5\), \(Q_3=13.5\), \(Max = 15\).
• For the data set \(1,2,4,5,6,7,9,10,11,11,12,13,13\): \(Min = 1\), \(Q_1=4.5\), \(Med = 9\), \(Q_3=12\), \(Max = 13\).