Question

5,5,6,9,10,14,16,16,16,17,17
min: □ q1: □ med: □ q3: □ max: □
create the box plot by dragging the lines:
box plot diagram with x - axis from 0 to 20

Explanation:

Step1: Find Min and Max

The minimum value is the smallest number, and the maximum is the largest. From the data \(5,5,6,9,10,14,16,16,16,17,17\), Min \(= 5\), Max \(= 17\).

Step2: Find Median (Med)

The data has \(n = 11\) values (odd). The median is the \(\frac{n + 1}{2}=6\)-th term. Sorting the data (already sorted), the 6th term is \(14\), so Med \(= 14\).

Step3: Find Q1 (First Quartile)

Q1 is the median of the lower half (values before the median). Lower half: \(5,5,6,9,10\) (5 values). Median of this is the 3rd term, so Q1 \(= 6\).

Step4: Find Q3 (Third Quartile)

Q3 is the median of the upper half (values after the median). Upper half: \(16,16,16,17,17\) (5 values). Median of this is the 3rd term, so Q3 \(= 16\).

Answer:

Min: \(5\), Q1: \(6\), Med: \(14\), Q3: \(16\), Max: \(17\)