Question

answer the statistical measures and create a box and whiskers plot for the following set of data. enter all values as whole numbers or decimals. 4,4,5,5,5,6,8,9,12,12,14,15,16,16 min: q1: med: q3: max: create the box plot by dragging the lines: answer attempt 1 out of 2 you must answer all questions above in order to submit.

Explanation:

Step1: Find the minimum and maximum

The minimum (Min) is the smallest value in the data set: \(4\).
The maximum (Max) is the largest value in the data set: \(16\).

Step2: Find the median (Med)

The data set has \(n = 14\) values. The median is the average of the \(\frac{n}{2}\) - th and \((\frac{n}{2}+ 1)\) - th values.
\(\frac{n}{2}=7\), \(\frac{n}{2}+1 = 8\). The \(7\) - th value is \(8\) and the \(8\) - th value is \(9\).
Median \(Med=\frac{8 + 9}{2}=8.5\)

Step3: Find the first quartile (Q1)

The lower half of the data set is \(4,4,5,5,5,6,8\). Since \(n_1=7\) (odd number of elements), \(Q1\) is the \(\frac{n_1 + 1}{2}\) - th value. \(\frac{7+1}{2}=4\) - th value. The \(4\) - th value of the lower half is \(5\)

Step4: Find the third quartile (Q3)

The upper half of the data set is \(12,12,14,15,16,16\). Since \(n_2 = 6\) (even number of elements), \(Q3\) is the average of the \(\frac{n_2}{2}\) - th and \((\frac{n_2}{2}+1)\) - th values. \(\frac{n_2}{2}=3\), \(\frac{n_2}{2}+1=4\). The \(3\) - rd value is \(14\) and the \(4\) - th value is \(15\). \(Q3=\frac{14 + 15}{2}=14.5\)

Answer:

Min: \(4\), Q1: \(5\), Med: \(8.5\), Q3: \(14.5\), Max: \(16\)