Ask a New Question
Menu

Which box-and-whisker plot represents this data: 6, 7, 8, 10, 18, 20, 22, 25, 28, 30, 30

?


A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 8 and 10 to 28 with a median between 20 and 22.


A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from 18 to between 24 and 26 with no median value.


A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 and between 26 and 28 with a median of 22.


A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 to between 26 and 28 with a median between 20 and 22.

1 answer

To determine which box-and-whisker plot represents the given data set: 6, 7, 8, 10, 18, 20, 22, 25, 28, 30, 30, we need to calculate the five-number summary, which includes:

  1. Minimum (smallest value)
  2. First quartile (Q1)
  3. Median (Q2)
  4. Third quartile (Q3)
  5. Maximum (largest value)

Given Data:

6, 7, 8, 10, 18, 20, 22, 25, 28, 30, 30

1. Minimum:

  • The minimum value is 6.

2. Maximum:

  • The maximum value is 30.

3. Median (Q2):

  • The data set has 11 numbers. The median is the middle number, which is the 6th value when the data is arranged in ascending order.
  • Median \( Q2 = 20 \).

4. First Quartile (Q1):

  • To find Q1, we take the first half of the data (the first 5 values): 6, 7, 8, 10, 18.
  • The median of this subset (5 values) is the 3rd value:
  • \( Q1 = 8 \).

5. Third Quartile (Q3):

  • For Q3, we take the second half of the data (the last 5 values): 20, 22, 25, 28, 30, 30.
  • The median of this subset (5 values) is the 3rd value:
  • \( Q3 = 25 \).

Summary:

Now we have the five-number summary:

  • Minimum = 6
  • Q1 = 8
  • Q2 (Median) = 20
  • Q3 = 25
  • Maximum = 30

Box-and-Whisker Plot Interpretation:

  1. The whiskers extend from 6 to 30.
  2. The box will range from 8 (Q1) to 25 (Q3).
  3. The median (Q2) is at 20.

Analyzing Options:

  1. First Option: Whiskers from 6 to 30, box from 8 to 10 to 28, with median between 20 and 22. (Incorrect Q3)
  2. Second Option: Whiskers from 6 to 30, box from 18 to 24 to 26, no median. (No correct Q1, Q2, Q3)
  3. Third Option: Whiskers from 6 to 30, box from 12 to 14 to 26 to 28, with median 22. (Incorrect Q1 and Q2)
  4. Fourth Option: Whiskers from 6 to 30, box from 12 to 14 to 26 to 28, median between 20 and 22. (Incorrect Q1 and Q3)

Conclusion:

None of the options completely match the calculated five-number summary and box-and-whisker plot characteristics.

However, you would expect the correct box-and-whisker plot to show:

  • Whiskers from 6 to 30.
  • Box from 8 to 25.
  • Median at 20.

Therefore, the first option is the best choice, though it incorrectly states the upper box limit. The median is also described inaccurately.