Which box-and-whisker plot represents the data set?

Question

11, 6, 19, 14, 21, 7, 13, 15, 15

Responses

A box and whisker plot. The whiskers range from 6 to 21 and the box ranges from 9 to 17 with the vertical bar inside the box at 14.
Image with alt text: A box and whisker plot. The whiskers range from 6 to 21 and the box ranges from 9 to 17 with the vertical bar inside the box at 14.

A box and whisker plot. The whiskers range from 6 to 21 and the box ranges from 11 to 19 with the vertical bar inside the box at 15.
Image with alt text: A box and whisker plot. The whiskers range from 6 to 21 and the box ranges from 11 to 19 with the vertical bar inside the box at 15.

A box and whisker plot. The whiskers range from 6 to 21 and the box ranges from 11 to 15 with the vertical bar inside the box at 14.
Image with alt text: A box and whisker plot. The whiskers range from 6 to 21 and the box ranges from 11 to 15 with the vertical bar inside the box at 14.

A box and whisker plot. The whiskers range from 6 to 21 and the box ranges from 7 to 19 with the vertical bar inside the box at 15.
Image with alt text: A box and whisker plot. The whiskers range from 6 to 21 and the box ranges from 7 to 19 with the vertical bar inside the box at 15.

Answer 1

To determine which box-and-whisker plot accurately represents the given data set (11, 6, 19, 14, 21, 7, 13, 15, 15), we need to calculate the five-number summary: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

1. Order the data:

   • 6, 7, 11, 13, 14, 15, 15, 19, 21

2. Minimum:

   • The smallest value is 6.

3. Maximum:

   • The largest value is 21.

4. Median (Q2):

   • The median is the middle value. For this set of 9 numbers, the median is the 5th number, which is 14.

5. Q1 (first quartile):

   • Q1 is the median of the first half of the data. The first half (6, 7, 11, 13) has a median between 7 and 11, which is 10.

6. Q3 (third quartile):

   • Q3 is the median of the second half of the data. The second half (15, 15, 19, 21) has a median between 15 and 19, which is 17.

Now we summarize our findings:

• Minimum: 6
• Q1: 10
• Median (Q2): 14
• Q3: 17
• Maximum: 21

Now we analyze the provided box-and-whisker plot options:

1. First option: Whiskers range from 6 to 21, box ranges from 9 to 17, vertical bar at 14.

   • Incorrect (Q1 should be 10).

2. Second option: Whiskers range from 6 to 21, box ranges from 11 to 19, vertical bar at 15.

   • Incorrect (Q1 is not correct, it should be 10).

3. Third option: Whiskers range from 6 to 21, box ranges from 11 to 15, vertical bar at 14.

   • Incorrect (Q3 is not 15, it should be 17).

4. Fourth option: Whiskers range from 6 to 21, box ranges from 7 to 19, vertical bar at 15.

   • Incorrect (Q1 is not right, should be 10).

None of the provided options match the calculated five-number summary. There may be an error in the options presented, as none accurately represent your provided dataset.