Question

based on the boxplot above (with data axis labeled 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18), identify the 5 number summary (min, q1, median, q3, max) five empty boxes, the inter - quatile range (iqr) = q3—q1 = empty box

Explanation:

Step1: Identify Minimum (min)

The leftmost whisker of the boxplot starts at 5, so min = 5.

Step2: Identify Q1 (First Quartile)

The left edge of the box is at 9, so Q1 = 9.

Step3: Identify Median

The line inside the box is at 9? Wait, no, looking at the boxplot, the box is from 7? Wait, no, the x - axis is marked from 5 to 18. Wait, the box starts at 7? Wait, no, the first vertical line of the box: the box has a left side at 7? Wait, no, the plot: the left whisker goes from 5 to 7, then the box starts at 7? Wait, no, the original plot: the first vertical line (min) is 5, then the left end of the box is at 7? Wait, no, the user's plot: the x - axis has marks at 5,6,7,8,9,10,11,12,13,14,15,16,17,18. The box starts at 7? Wait, no, the left side of the box is at 7? Wait, no, the first part of the box (Q1) is at 9? Wait, no, let's re - examine. The boxplot: the left whisker is from 5 to 7 (the left end of the box is at 7? No, the box is a rectangle. The left edge of the box is at 7? Wait, no, the vertical lines: the min is at 5, the left end of the box (Q1) is at 9? Wait, no, the box is divided into two parts. Wait, the first quartile (Q1) is the left edge of the box, the median is the line inside the box, the third quartile (Q3) is the right edge of the box, and the max is the rightmost whisker.

Looking at the plot: the left whisker starts at 5 (min), the left edge of the box (Q1) is at 9? Wait, no, the box is from 7 to 15? Wait, no, the x - axis marks: 5,6,7,8,9,10,11,12,13,14,15,16,17,18. The box is a rectangle with left side at 7? No, the first vertical line of the box: the left end of the box is at 7? Wait, the user's plot: the box is drawn from 7 to 15? Wait, no, the left whisker is from 5 to 7, the box is from 7 to 15, with a line at 9 (median)? No, wait, the box has a vertical line at 9 (median), so the box is split into two parts. So:

- Min: The leftmost point of the whisker, which is 5.
- Q1: The left edge of the box. Looking at the x - axis, the left edge of the box is at 7? Wait, no, the x - axis labels: 5,6,7,8,9,10,11,12,13,14,15,16,17,18. The box starts at 7? No, the first vertical line of the box is at 7? Wait, the left whisker is from 5 to 7 (so min = 5, and the left end of the box is 7 (Q1)? Then the median is at 9? The right end of the box (Q3) is at 15? And the max is 18.

Wait, let's correct:

- Min: The smallest value, which is the left end of the left whisker, so 5.
- Q1: The first quartile, which is the left edge of the box. From the plot, the left edge of the box is at 7? Wait, no, the box is a rectangle. Let's look at the x - axis ticks. The left whisker goes from 5 to 7 (so min = 5, and the left end of the box is 7 (Q1)). Then the median (the line inside the box) is at 9. The right end of the box (Q3) is at 15. The right whisker goes from 15 to 18, so max = 18.

Then IQR = Q3 - Q1 = 15 - 7 = 8? Wait, no, maybe I misread the box. Wait, the box is divided into two parts. The left part of the box (from Q1 to median) and the right part (median to Q3). Let's re - examine the plot:

The box is drawn from 7 to 15? No, the x - axis has marks at 5,6,7,8,9,10,11,12,13,14,15,16,17,18. The left edge of the box is at 7, the median line is at 9, the right edge of the box is at 15, the left whisker is from 5 to 7, the right whisker is from 15 to 18.

So:

- Min: 5
- Q1: 7
- Median: 9
- Q3: 15
- Max: 18

Then IQR = Q3 - Q1 = 15 - 7 = 8. Wait, but maybe the left edge of the box is at 9? Wait, the box is a rectangle with a vertical line at 9 (median). So the left half of the box is from Q1 to median, and the right half from median to Q3. Let's look at the x - axis: the box starts at 7? No, the first vertical line of the box is at 7? Wait, the user's plot: the left whisker is from 5 to 7, then the box is from 7 to 15, with a median at 9. So:

Step1: Min

The leftmost whisker end is at 5, so min = 5.

Step2: Q1

The left edge of the box is at 7, so Q1 = 7.

Step3: Median

The line inside the box is at 9, so median = 9.

Step4: Q3

The right edge of the box is at 15, so Q3 = 15.

Step5: Max

The rightmost whisker end is at 18, so max = 18.

Step6: IQR

IQR = Q3 - Q1 = 15 - 7 = 8.

Answer:

5, 7, 9, 15, 18
The Inter - Quatile Range (IQR) = 8