Question

which data set could be represented by the box plot shown below? choose 1 answer: a 3,4,8,9,9,12,12,13,13,16,18 b 3,4,7,9,9,10,12,13,13,16,18 c 2,4,7,9,9,10,12,13,13,16,18 d 3,4,8,9,9,10,12,13,13,16,18

Explanation:

Step1: Analyze the box plot's minimum, Q1, median, Q3, maximum

From the box plot, the minimum (left whisker end) is 3 (since the left dot is at 3), Q1 (start of box) around 7 - 8? Wait, no, let's check the data sets. Wait, the box plot: left dot at 3, right dot at 18. The box has two parts, so median is between 9 - 10? Wait, let's list the data sets. Each data set has 11 elements (since 11 numbers). So for a data set with \( n = 11 \) (odd), the median is the 6th term (since \( (11 + 1)/2 = 6 \)). Q1 is the median of the first 5 terms, Q3 is the median of the last 5 terms.

Step2: Check each option's minimum, median, Q1, Q3, maximum

- **Option A**: Data: 3,4,8,9,9,12,12,13,13,16,18
Minimum: 3, Maximum: 18.
Median (6th term): 12.
Q1 (median of first 5: 3,4,8,9,9) → 8.
Q3 (median of last 5: 12,13,13,16,18) → 13.
But box plot's median seems around 10? Wait, maybe I misread. Wait the box plot: the box is split, so maybe median is between 9 and 10? Wait no, let's check the x - axis. The box starts around 7? Wait no, the left dot is at 3 (x = 3), then the whisker to the box. The box has two parts, so the first quartile (Q1), median (Q2), third quartile (Q3). Let's check each option's median (6th term):

- **Option B**: 3,4,7,9,9,10,12,13,13,16,18
Median (6th term): 10.
Q1 (first 5: 3,4,7,9,9) → 7.
Q3 (last 5: 12,13,13,16,18) → 13.
Minimum: 3, Maximum: 18.

- **Option C**: 2,4,7,9,9,10,12,13,13,16,18
Minimum: 2 (but box plot's minimum is 3, so eliminate C).

- **Option D**: 3,4,8,9,9,10,12,13,13,16,18
Median (6th term): 10.
Q1 (first 5: 3,4,8,9,9) → 8.
Q3 (last 5: 12,13,13,16,18) → 13.
Minimum: 3, Maximum: 18.

Wait, the box plot: the left whisker starts at 3, then the box. Let's check the box's left edge (Q1) and right edge (Q3). Let's see the x - axis: 0,2,4,6,8,10,12,14,16,18,20. The box is between, say, 7 - 13? Wait no, the box has two parts, so maybe Q1 is 7 (Option B) or 8 (Option D). Wait the left dot is at 3, right at 18. Let's check the data points:

Wait the box plot: the left whisker is from 3 to Q1, box from Q1 to Q3, right whisker from Q3 to 18. The box is split, so median is at the middle of the box. Let's check the median of each option:

Option A: median 12 (6th term is 12) → box would be around 8 - 13, median 12. But the box plot's median seems lower.

Option B: median 10 (6th term 10) → box from 7 (Q1) to 13 (Q3), median 10.

Option D: median 10 (6th term 10), Q1 8, Q3 13.

Wait the left whisker: from 3 to Q1. In Option B, Q1 is 7 (median of first 5: 3,4,7,9,9 → 7). In Option D, Q1 is 8 (median of first 5: 3,4,8,9,9 → 8). Looking at the box plot, the left end of the box (Q1) is around 7? Let's check the x - axis marks: 0,2,4,6,8,10,12,14,16,18,20. The left dot is at 3, then the whisker to the box. The box starts at, say, 7 (since 6 is a mark, 7 is between 6 and 8). So Q1 = 7. Then Option B has Q1 = 7, Option D has Q1 = 8. So Option B: first 5 terms 3,4,7,9,9 → median 7 (Q1 = 7). Then the box from 7 to 13 (Q3 = 13), median 10 (6th term). The left whisker from 3 to 7, right whisker from 13 to 18. Let's check the data points:

Option B: 3,4,7,9,9,10,12,13,13,16,18. Minimum 3, maximum 18, Q1 = 7, median = 10, Q3 = 13. This matches the box plot: left dot at 3, Q1 at 7, median at 10, Q3 at 13, right dot at 18.

Wait but let's re - check Option D: 3,4,8,9,9,10,12,13,13,16,18. Q1 is 8 (median of first 5: 3,4,8,9,9). So the box would start at 8, but the box plot's box starts before 8 (around 7). So Option B is better. Wait no, maybe I made a mistake. Wait the first 5 terms of Option B: 3,4,7,9,9. The median of these 5 is the 3rd term, which is 7. So Q1 = 7. The 6th term is 10 (median). The last 5 terms: 12,13,13,16,18. Median is 13 (Q3 = 13). So the box is from 7 to 13, median at 10. The left whisker from 3 to 7, right whisker from 13 to 18. This matches the box plot: left dot at 3, box starts at 7, median at 10, box ends at 13, right dot at 18.

Option D: first 5 terms 3,4,8,9,9 → median 8 (Q1 = 8). So box starts at 8, but the box plot's box starts at 7 (since the x - axis mark at 6, then 7, then 8). So Option B's Q1 = 7 is closer to the box plot's left box edge. Also, Option C has minimum 2, which is wrong (box plot's minimum is 3). Option A has median 12, which is too high. So the correct answer is B.

Answer:

B. 3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18