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. 5,9,9,10,12,13,15,16,17,17 min □ q1 □ med □ q3 □ max □ create the box plot by dragging the lines: box plot image 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: \(5, 9, 9, 10, 12, 13, 15, 16, 17, 17\)
Min: \(5\), Max: \(17\)

Step2: Find Median (Med)

The data set has \(n = 10\) values (even number). The median is the average of the \(\frac{n}{2}\)-th and \((\frac{n}{2}+1)\)-th values when sorted.
Sorted data: \(5, 9, 9, 10, 12, 13, 15, 16, 17, 17\)
\(\frac{n}{2}=5\)-th value: \(12\), \((\frac{n}{2}+1)=6\)-th value: \(13\)
Median: \(\frac{12 + 13}{2}=12.5\)

Step3: Find Q1 (First Quartile)

Q1 is the median of the lower half of the data (excluding the median if \(n\) is even? Wait, for \(n = 10\), lower half is first 5 values: \(5, 9, 9, 10, 12\))
Median of lower half (5 values, odd number, so 3rd value): \(9\)
So Q1: \(9\)

Step4: Find Q3 (Third Quartile)

Q3 is the median of the upper half of the data (upper 5 values: \(13, 15, 16, 17, 17\))
Median of upper half (5 values, odd number, so 3rd value): \(16\)
So Q3: \(16\)

Answer:

Min: \(5\), Q1: \(9\), Med: \(12.5\), Q3: \(16\), Max: \(17\)

For the box - and - whisker plot:

• The left whisker extends from Min (\(5\)) to Q1 (\(9\)).
• The box extends from Q1 (\(9\)) to Q3 (\(16\)), with a line inside the box at the median (\(12.5\)).
• The right whisker extends from Q3 (\(16\)) to Max (\(17\)).