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. 6,6,8,9,10,11,14,19 min: □ q1: □ med: □ q3: □ max: □ create the box plot by dragging the lines: box plot image with x - axis from 0 to 20, labeled 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20

Explanation:

Step1: Find Minimum (Min)

The minimum value is the smallest number in the data set.
Data set: \(6, 6, 8, 9, 10, 11, 14, 19\)
So, Min = \(6\)

Step2: Find Maximum (Max)

The maximum value is the largest number in the data set.
Data set: \(6, 6, 8, 9, 10, 11, 14, 19\)
So, Max = \(19\)

Step3: Find Median (Med)

First, the data is already ordered. Since there are 8 (even) data points, the median is the average of the 4th and 5th values.
4th value: \(9\), 5th value: \(10\)
Median = \(\frac{9 + 10}{2} = 9.5\)

Step4: Find Q1 (First Quartile)

Q1 is the median of the lower half of the data. The lower half is \(6, 6, 8, 9\) (first 4 values).
Since there are 4 (even) values, the median of the lower half is the average of the 2nd and 3rd values.
2nd value: \(6\), 3rd value: \(8\)
Q1 = \(\frac{6 + 8}{2} = 7\)

Step5: Find Q3 (Third Quartile)

Q3 is the median of the upper half of the data. The upper half is \(10, 11, 14, 19\) (last 4 values).
Since there are 4 (even) values, the median of the upper half is the average of the 2nd and 3rd values.
2nd value: \(11\), 3rd value: \(14\)
Q3 = \(\frac{11 + 14}{2} = 12.5\)

Answer:

Min: \(6\)
Q1: \(7\)
Med: \(9.5\)
Q3: \(12.5\)
Max: \(19\)

For the box - and - whisker plot:

• The left whisker extends from Min (\(6\)) to Q1 (\(7\)).
• The box extends from Q1 (\(7\)) to Q3 (\(12.5\)), with a line inside the box at the median (\(9.5\)).
• The right whisker extends from Q3 (\(12.5\)) to Max (\(19\)).