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. 1,3,3,5,6,6,6,7,7,10,10,11,14 min q1 med q3 max create the box plot by dragging the lines.

Explanation:

Step1: Order the data (already ordered)

Data: \(1, 3, 3, 5, 6, 6, 6, 7, 7, 10, 10, 11, 14\)

Step2: Find Min and Max

Min is the smallest value: \(1\)
Max is the largest value: \(14\)

Step3: Find Median (Q2)

Number of data points \(n = 13\) (odd), so median is the \(\frac{13 + 1}{2}=7\)-th term.
7 -th term: \(6\) (Median = \(6\))

Step4: Find Q1 (median of lower half)

Lower half: \(1, 3, 3, 5, 6, 6\) (6 data points, even)
Median of lower half: \(\frac{3 + 5}{2}=4\) (Q1 = \(4\))

Step5: Find Q3 (median of upper half)

Upper half: \(7, 7, 10, 10, 11, 14\) (6 data points, even)
Median of upper half: \(\frac{10 + 10}{2}=10\) (Q3 = \(10\))

Answer:

Min: \(1\)
Q1: \(4\)
Med: \(6\)
Q3: \(10\)
Max: \(14\)

For the box - and - whiskers plot:

• The left whisker extends from Min (\(1\)) to Q1 (\(4\)).
• The box extends from Q1 (\(4\)) to Q3 (\(10\)), with a line inside the box at the Median (\(6\)).
• The right whisker extends from Q3 (\(10\)) to Max (\(14\)).