Question

2,2,5,6,8,10,10,10,15,16,17,18,19

min: □ q1: □ med: □ q3: □ max: □

create the box plot by dragging the lines:

box plot diagram with number line 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 set \(2,2,5,6,8,10,10,10,15,16,17,18,19\), Min = \(2\), Max = \(19\).

Step2: Find Median (Med)

The data set has \(n = 13\) values (odd number). The median is the \(\frac{n + 1}{2}=\frac{13+1}{2}=7\)-th term. The 7th term is \(10\), so Med = \(10\).

Step3: Find Q1 (First Quartile)

Q1 is the median of the lower half (excluding the median if \(n\) is odd). The lower half is \(2,2,5,6,8,10\) (6 values, even). The median of this is the average of the 3rd and 4th terms: \(\frac{5 + 6}{2}=5.5\), so Q1 = \(5.5\).

Step4: Find Q3 (Third Quartile)

Q3 is the median of the upper half (excluding the median if \(n\) is odd). The upper half is \(10,15,16,17,18,19\) (6 values, even). The median of this is the average of the 3rd and 4th terms: \(\frac{16 + 17}{2}=16.5\), so Q3 = \(16.5\).

Answer:

Min: \(2\), Q1: \(5.5\), Med: \(10\), Q3: \(16.5\), Max: \(19\)