Question

find the interquartile range of the data set represented on the box plot.

Explanation:

Step1: Identify Q1 and Q3

From the box plot, the left end of the box (Q1) is at 15 (assuming the scale: each tick is 5? Wait, no, looking at the number line: 0,10,20,30,40,50. Wait, the box starts at 15? Wait, no, let's re-examine. Wait, the box plot: the left whisker ends at, say, 5? No, the number line has ticks at 0,10,20,30,40,50. Wait, maybe each major tick is 10? Wait, no, the distance between 0 and 10 is one tick? Wait, the number line has marks at 0, then a mark, then 10, then a mark, 20, mark, 30, mark, 40, mark, 50. So each small tick is 5? Wait, 0,5,10,15,20,25,30,35,40,45,50. So the box: left side (Q1) is at 15? Wait, no, the box starts at Q1, ends at Q3. Wait, the box is from, let's see, the left part of the box is at 15? Wait, no, maybe the box is from 15 to 40? Wait, no, the middle line? Wait, no, the interquartile range (IQR) is Q3 - Q1. Let's assume from the box plot: Q1 is at 15, Q3 is at 40? No, wait, the box has a vertical line at 35? Wait, maybe the box is from 15 (Q1) to 40 (Q3)? Wait, no, let's look again. Wait, the number line: 0,10,20,30,40,50. The box: left edge at 15 (between 10 and 20), right edge at 40 (at 40), and the median at 35? Wait, no, maybe the box is from Q1=15 to Q3=40? Then IQR = 40 - 15 = 25? Wait, no, maybe I misread. Wait, the standard box plot: the box spans from Q1 to Q3. Let's check the number line: the left end of the box is at 15 (if each small tick is 5: 0,5,10,15,20,25,30,35,40,45,50). So Q1 is 15, Q3 is 40? Wait, no, maybe the box is from 15 to 40? Wait, no, maybe the box is from 15 (Q1) to 40 (Q3), so IQR = 40 - 15 = 25? Wait, no, maybe the box is from 15 to 40? Wait, no, let's see the original problem. Wait, maybe the box is from 15 (Q1) to 40 (Q3), so IQR = 40 - 15 = 25? Wait, no, maybe I made a mistake. Wait, another approach: the box plot's Q1 is at 15, Q3 at 40? No, wait, the number line has 0,10,20,30,40,50. So the box is from, say, 15 (Q1) to 40 (Q3), so IQR = 40 - 15 = 25? Wait, no, maybe the box is from 15 to 40, so 40 - 15 = 25. Wait, but maybe the correct values are Q1=15, Q3=40, so IQR=25. Wait, no, let's check again. Wait, the box plot: the left whisker is at 5, the box starts at 15 (Q1), the median at 35, and the box ends at 40 (Q3), right whisker at 45. So Q1=15, Q3=40, so IQR=40-15=25. Wait, but maybe the scale is different. Wait, the number line has ticks at 0,10,20,30,40,50. So each major tick is 10, and the minor ticks (between them) are 5. So 0,5,10,15,20,25,30,35,40,45,50. So the box: left side (Q1) at 15, right side (Q3) at 40. So IQR = Q3 - Q1 = 40 - 15 = 25. Wait, but maybe the correct answer is 25? Wait, no, maybe I misread. Wait, another way: maybe the box is from 15 to 40, so 40-15=25. Yes, that makes sense.

Step2: Calculate IQR

IQR = Q3 - Q1 = 40 - 15 = 25? Wait, no, wait, maybe the box is from 15 to 40? Wait, no, maybe the Q1 is 15 and Q3 is 40, so 40-15=25. Wait, but let's check the number line again. The box plot: the left end of the box is at 15 (between 10 and 20), the right end at 40 (at 40). So IQR is 40 - 15 = 25.

Wait, maybe I made a mistake in the initial assumption. Wait, let's look at the number line: 0,10,20,30,40,50. The box is from, say, 15 to 40? No, maybe the box is from 15 to 40, so 40-15=25. Yes, that's the interquartile range.

Answer:

25