Question

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.
2,2,3,4,5,5,8,8,10,10,11,13,15,15,15
min: □ q1: □ med: □ q3: □ max: □
create the box plot by dragging the lines:
box plot template with x-axis from 0 to 20

Explanation:

Step1: Find Min and Max

The minimum value (Min) is the smallest number in the data set, and the maximum value (Max) is the largest.
Data: \(2, 2, 3, 4, 5, 5, 8, 8, 10, 10, 11, 13, 15, 15, 15\)
Min: \(2\)
Max: \(15\)

Step2: Find Median (Med)

The median is the middle value when the data is ordered. There are \(n = 15\) data points, so the median is the \(\frac{15 + 1}{2}= 8^{\text{th}}\) value.
Ordered data: \(2, 2, 3, 4, 5, 5, 8, \boldsymbol{8}, 10, 10, 11, 13, 15, 15, 15\)
Med: \(8\)

Step3: Find Q1 (First Quartile)

Q1 is the median of the lower half of the data (excluding the median if \(n\) is odd). The lower half is the first \(7\) values: \(2, 2, 3, 4, 5, 5, 8\). The median of these \(7\) values is the \(\frac{7 + 1}{2}= 4^{\text{th}}\) value.
Lower half: \(2, 2, 3, \boldsymbol{4}, 5, 5, 8\)
Q1: \(4\)

Step4: Find Q3 (Third Quartile)

Q3 is the median of the upper half of the data (excluding the median if \(n\) is odd). The upper half is the last \(7\) values: \(10, 10, 11, 13, 15, 15, 15\). The median of these \(7\) values is the \(\frac{7 + 1}{2}= 4^{\text{th}}\) value.
Upper half: \(10, 10, 11, \boldsymbol{13}, 15, 15, 15\)
Q3: \(13\)

Answer:

Min: \(2\), Q1: \(4\), Med: \(8\), Q3: \(13\), Max: \(15\)