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.

3,4,4,6,6,8,9,12,15

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 (Min) is the smallest number in the data set, and the maximum value (Max) is the largest.
Data: 3, 4, 4, 6, 6, 8, 9, 12, 15
Min = 3, Max = 15

Step2: Find Median (Med)

The median is the middle value when the data is ordered. There are 9 data points, so the 5th value (since \((9 + 1)/2 = 5\)) is the median.
Ordered data: 3, 4, 4, 6, 6, 8, 9, 12, 15
Med = 6

Step3: Find Q1 (First Quartile)

Q1 is the median of the lower half (excluding the median if odd number of data points). Lower half: 3, 4, 4, 6 (4 data points). The median of these is the average of the 2nd and 3rd values.
\(Q1=\frac{4 + 4}{2}=4\)

Step4: Find Q3 (Third Quartile)

Q3 is the median of the upper half (excluding the median if odd number of data points). Upper half: 8, 9, 12, 15 (4 data points). The median of these is the average of the 2nd and 3rd values.
\(Q3=\frac{9 + 12}{2}=10.5\)

Answer:

Min: \(3\)
Q1: \(4\)
Med: \(6\)
Q3: \(10.5\)
Max: \(15\)

For the box - and - whisker plot:

• The left whisker extends from Min (\(3\)) to Q1 (\(4\)).
• The box extends from Q1 (\(4\)) to Q3 (\(10.5\)), with a line inside the box at the median (\(6\)).
• The right whisker extends from Q3 (\(10.5\)) to Max (\(15\)).