Question

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

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 set: \(5, 6, 7, 9, 10, 11, 12, 12, 14, 15, 16, 17, 18, 19\)
Min: \(5\), Max: \(19\)

Step2: Find the Median (Med)

The data set has \(n = 14\) 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: \(5, 6, 7, 9, 10, 11, 12, 12, 14, 15, 16, 17, 18, 19\)
\(\frac{n}{2}=7\)-th value: \(12\), \((\frac{n}{2}+1)=8\)-th value: \(12\)
Med: \(\frac{12 + 12}{2}=12\)

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 \(n = 14\), lower half is first 7 values: \(5, 6, 7, 9, 10, 11, 12\)
Median of lower half (7 values, odd number): the \(\frac{7 + 1}{2}=4\)-th value.
Sorted lower half: \(5, 6, 7, 9, 10, 11, 12\)
4-th value: \(9\)? Wait, no: positions 1:5, 2:6, 3:7, 4:9, 5:10, 6:11, 7:12. So median (Q1) is 9? Wait, no, wait: when \(n\) is even, for quartiles, sometimes we take the lower half as first \(n/2\) values. Wait, \(n = 14\), so lower half is first 7 values (indices 0 - 6 if 0 - based), upper half is last 7 values (indices 7 - 13). Wait, no, the data is \(5,6,7,9,10,11,12,12,14,15,16,17,18,19\). So lower half (before median) is first 7 numbers: \(5,6,7,9,10,11,12\). The median of this lower half: since there are 7 numbers, the median is the 4th number (since \((7 + 1)/2 = 4\)). So 4th number in lower half: \(5\) (1), \(6\) (2), \(7\) (3), \(9\) (4). So Q1 is \(9\)? Wait, no, wait, maybe I made a mistake. Wait, let's list the positions:

Data points (sorted): 1:5, 2:6, 3:7, 4:9, 5:10, 6:11, 7:12, 8:12, 9:14, 10:15, 11:16, 12:17, 13:18, 14:19.

Median is between 7th and 8th: (12 + 12)/2 = 12. Correct.

Q1: median of first 7 data points (1 - 7): 1:5, 2:6, 3:7, 4:9, 5:10, 6:11, 7:12. The median of these 7 is the 4th term: 9.

Q3: median of last 7 data points (8 - 14): 8:12, 9:14, 10:15, 11:16, 12:17, 13:18, 14:19. The median of these 7 is the 11th term? Wait, no, 8 - 14 is 7 terms: positions 8 (12), 9 (14), 10 (15), 11 (16), 12 (17), 13 (18), 14 (19). The median is the 11th term? Wait, no, the number of terms is 7, so the median is the \((7 + 1)/2 = 4\)-th term in this sub - set. So 8:12 (1), 9:14 (2), 10:15 (3), 11:16 (4). So Q3 is 16.

Let's verify:

• Min: 5 (smallest value)
• Q1: median of lower half (first 7 values: 5,6,7,9,10,11,12). The middle value (4th) is 9.
• Med: median of all 14 values, average of 7th and 8th (12 and 12) is 12.
• Q3: median of upper half (last 7 values: 12,14,15,16,17,18,19). The middle value (4th) is 16.
• Max: 19 (largest value)

Answer:

Min: \(5\), Q1: \(9\), Med: \(12\), Q3: \(16\), Max: \(19\)