Question

question
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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.
2,2,3,3,6,9,10,14,14,18,19
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 (Min) is the smallest value, and the maximum (Max) is the largest value in the data set.
Data set: \(2, 2, 3, 3, 6, 9, 10, 14, 14, 18, 19\)
Min: \(2\)
Max: \(19\)

Step2: Find Median (Med)

The median is the middle value when the data is ordered. Since there are \(11\) values (odd number), the median is the \(\frac{11 + 1}{2}=6\)-th value.
Ordered data: \(2, 2, 3, 3, 6, 9, 10, 14, 14, 18, 19\)
6th value: \(9\)
So, Med: \(9\)

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 \(2, 2, 3, 3, 6\) (5 values). The median of this set is the 3rd value.
Lower half: \(2, 2, 3, 3, 6\)
3rd value: \(3\)
So, Q1: \(3\)

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 \(10, 14, 14, 18, 19\) (5 values). The median of this set is the 3rd value.
Upper half: \(10, 14, 14, 18, 19\)
3rd value: \(14\)
So, Q3: \(14\)

Answer:

Min: \(2\)
Q1: \(3\)
Med: \(9\)
Q3: \(14\)
Max: \(19\)

For the box - and - whisker plot:

• The left whisker extends from Min (\(2\)) to Q1 (\(3\)).
• The box extends from Q1 (\(3\)) to Q3 (\(14\)), with a line inside the box at the median (\(9\)).
• The right whisker extends from Q3 (\(14\)) to Max (\(19\)).