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.
3,5,5,8,9,10,10,12,12,12,13,14,14,16
min: q1: med: q3: max:
create the box plot by dragging the lines:

Explanation:

Step1: Find Min and Max

The minimum (Min) is the smallest value in the data set. The maximum (Max) is the largest value.
For the data set \(3,5,5,8,9,10,10,12,12,12,13,14,14,16\), \(Min = 3\) and \(Max=16\).

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 when \(n\) is even.
\(\frac{n}{2}=7\), \(\frac{n}{2}+1 = 8\). The 7 - th value is \(10\) and the 8 - th value is \(12\).
\(Med=\frac{10 + 12}{2}=11\).

Step3: Find Q1

Q1 is the median of the lower half of the data. The lower half of the data is \(3,5,5,8,9,10,10\). Since \(n_1=7\) (odd), the median of the lower half (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 \(8\).

Step4: Find Q3

Q3 is the median of the upper half of the data. The upper half of the data is \(12,12,13,14,14,16\). Since \(n_2 = 6\) (even), \(Q3=\frac{13+14}{2}=13.5\).

Answer:

Min: \(3\), Q1: \(8\), Med: \(11\), Q3: \(13.5\), Max: \(16\)