Question

1. fill in the values below and use them to create a box and whiskers plot for the following set of data. 3,4,5,8,9,13,13,13,14,14,14,17,18,18 min: q1: _ med: _ q3: ___ max:

Explanation:

Step1: Find the minimum and maximum values

The minimum value (Min) is the smallest number in the data set. The maximum value (Max) is the largest number in the data set.
For the data set \(3,4,5,8,9,13,13,13,14,14,14,17,18,18\), Min \( = 3\) and Max \(=18\).

Step2: Find the median (Med)

The median is the middle value of a sorted data set. Since there are \(n = 14\) data points (\(n\) is even), the median is the average of the \(\frac{n}{2}\) - th and \((\frac{n}{2}+1)\) - th values.
\(\frac{n}{2}=7\) and \(\frac{n}{2}+1 = 8\). The 7 - th value is \(13\) and the 8 - th value is \(13\). So, Med \(=\frac{13 + 13}{2}=13\).

Step3: Find the first quartile (Q1)

The first quartile \(Q1\) is the median of the lower half of the data. The lower half of the data is \(3,4,5,8,9,13,13\). Since \(n_1=7\) (odd), \(Q1\) is the \(\frac{n_1 + 1}{2}\) - th value. \(\frac{7+1}{2}=4\). The 4 - th value of the lower half is \(8\).

Step4: Find the third quartile (Q3)

The third quartile \(Q3\) is the median of the upper half of the data. The upper half of the data is \(14,14,14,17,18,18\). Since \(n_2 = 7\) (odd), \(Q3\) is the \(\frac{n_2+1}{2}\) - th value. \(\frac{7 + 1}{2}=4\). The 4 - th value of the upper half is \(17\).

Answer:

Min: \(3\), Q1: \(8\), Med: \(13\), Q3: \(17\), Max: \(18\)