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. 5,6,8,9,9,9,10,10,11,13,13,16,19 min: □ q1: □ med: □ q3: □ max: □ create the box plot by dragging the lines: box plot image you must answer all questions above in order to submit. attempt 1 out of 10

Explanation:

Step1: Find Min and Max

The data set is \(5,6,8,9,9,9,10,10,11,13,13,16,19\). The minimum value (Min) is the smallest number, which is \(5\). The maximum value (Max) is the largest number, which is \(19\).

Step2: Find Median (Med)

The number of data points \(n = 13\) (odd). The median is the middle value. For \(n = 13\), the middle position is \(\frac{n + 1}{2}=\frac{13+ 1}{2}=7\)th term. The 7th term in the ordered data set is \(10\), so Med \(= 10\).

Step3: Find Q1 (First Quartile)

Q1 is the median of the lower half of the data. The lower half is the data before the median: \(5,6,8,9,9,9\) (6 data points, even). The median of these 6 points is the average of the 3rd and 4th terms. 3rd term: \(8\), 4th term: \(9\). So \(Q1=\frac{8 + 9}{2}=8.5\).

Step4: Find Q3 (Third Quartile)

Q3 is the median of the upper half of the data. The upper half is the data after the median: \(11,13,13,16,19\)? Wait, no, original data after median (7th term is 10) is \(11,13,13,16,19\)? Wait, no, the data set is \(5,6,8,9,9,9,10,10,11,13,13,16,19\). So upper half (after 7th term) is \(11,13,13,16,19\)? Wait, no, when \(n = 13\), the lower half is first 6 terms (\(5,6,8,9,9,9\)) and upper half is last 6 terms (\(11,13,13,16,19\)? Wait, no, 7th term is 10, so upper half is from 8th term to 13th term: \(11,13,13,16,19\)? Wait, no, 8th term is 10? Wait, no, ordered data: positions 1:5, 2:6, 3:8, 4:9, 5:9, 6:9, 7:10, 8:10, 9:11, 10:13, 11:13, 12:16, 13:19. Oh, I made a mistake earlier. The upper half is from position 8 to 13: \(10,11,13,13,16,19\) (6 data points). The median of these 6 points is the average of the 3rd and 4th terms. 3rd term: \(13\), 4th term: \(13\). So \(Q3=\frac{13 + 13}{2}=13\). Wait, no, wait the lower half: positions 1 - 6: \(5,6,8,9,9,9\) (6 terms), median of lower half: average of 3rd (\(8\)) and 4th (\(9\)): \(\frac{8 + 9}{2}=8.5\) (correct for Q1). Upper half: positions 8 - 13: \(10,11,13,13,16,19\)? Wait, no, position 7 is 10, so upper half is positions 8 - 13: 8th term is 10? No, 7th term is 10, 8th term is 10, 9th is 11, 10th is 13, 11th is 13, 12th is 16, 13th is 19. So upper half data: \(10,11,13,13,16,19\) (6 terms). The median of these is average of 3rd (\(13\)) and 4th (\(13\)): \(13\). So Q3 \(= 13\).

Answer:

Min: \(5\), Q1: \(8.5\), Med: \(10\), Q3: \(13\), Max: \(19\)

For the box - and - whiskers plot:

• The left whisker starts at Min (\(5\)) and ends at Q1 (\(8.5\)).
• The box starts at Q1 (\(8.5\)), has a line at Med (\(10\)), and ends at Q3 (\(13\)).
• The right whisker starts at Q3 (\(13\)) and ends at Max (\(19\)).