Question

1. fill in the values below and use them to create a box and whiskers plot for the following set of data. 5,6,6,7,8,8,9,10,11,12,13,14,14,15,15 min: 5 q1: _ med: _ q3: _ max: 15 8. fill in the values below and use them to create a box and whiskers plot for the following set of data. 5,6,6,7,8,8,8,8,9,9,10,15,16,17,17 min: _ q1: _ med: _ q3: _ max: _

Explanation:

Step1: Find Min and Max

The minimum (Min) is the smallest value in the data set.
For the first data set \(5,6,6,7,8,8,9,10,11,12,13,14,14,15,15\), Min \( = 5\).
For the second data set \(5,6,6,7,8,8,8,8,9,9,10,15,16,17,17\), Min \(=5\).
The maximum (Max) is the largest value in the data set.
For the first data set, Max \( = 15\).
For the second data set, Max \(=17\).

Step2: Find the median (Med)

The median is the middle value. If \(n\) (number of data points) is odd, \(Med=(\frac{n + 1}{2})^{th}\) value. If \(n\) is even, \(Med=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}}{2}\) value.
For the first data set, \(n = 15\) (odd). \(\frac{15+ 1}{2}=8^{th}\) value. The \(8^{th}\) value is \(10\), so \(Med = 10\).
For the second data set, \(n = 15\) (odd). \(\frac{15 + 1}{2}=8^{th}\) value. The \(8^{th}\) value is \(8\), so \(Med = 8\).

Step3: Find Q1 and Q3

Q1 is the median of the lower half of the data. Q3 is the median of the upper half of the data.
For the first data set:
The lower half is \(5,6,6,7,8,8,9\) (\(n_1=7\) (odd)). \(\frac{7+1}{2}=4^{th}\) value. Q1 \(=7\).
The upper half is \(11,12,13,14,14,15,15\) (\(n_2 = 7\) (odd)). \(\frac{7+1}{2}=4^{th}\) value. Q3 \(=14\).
For the second data set:
The lower half is \(5,6,6,7,8,8,8\) (\(n_1=7\) (odd)). \(\frac{7+1}{2}=4^{th}\) value. Q1 \(=7\).
The upper half is \(9,9,10,15,16,17,17\) (\(n_2=7\) (odd)). \(\frac{7+1}{2}=4^{th}\) value. Q3 \(=15\).

Answer:

1. Min: \(5\), Q1: \(7\), Med: \(10\), Q3: \(14\), Max: \(15\)
2. Min: \(5\), Q1: \(7\), Med: \(8\), Q3: \(15\), Max: \(17\)