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Which of the following box plots matches the data set below?

15, 20, 20, 25, 26, 28, 28, 30, 32

(1 point)

3 answers

To create a box plot for the data set you provided, we first need to find the five-number summary: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

  1. Arrange the Data (already ordered):

    • 15, 20, 20, 25, 26, 28, 28, 30, 32

  2. Find the Minimum and Maximum:

    • Minimum (Min) = 15
    • Maximum (Max) = 32

  3. Find the Median (Q2):

    • The median is the middle number in the data set. Since there are 9 numbers, the median is the 5th number:
    • Median (Q2) = 26

  4. Find the First Quartile (Q1):

    • Q1 is the median of the first half of the data (the first four numbers):
    • First half: 15, 20, 20, 25
    • Median of this half = (20 + 20) / 2 = 20
    • Q1 = 20

  5. Find the Third Quartile (Q3):

    • Q3 is the median of the second half of the data (the last four numbers):
    • Second half: 28, 28, 30, 32
    • Median of this half = (28 + 30) / 2 = 29
    • Q3 = 29

  6. Summary:

    • Minimum (Min) = 15
    • Q1 = 20
    • Median (Q2) = 26
    • Q3 = 29
    • Maximum (Max) = 32

Now, you can match this five-number summary to the box plots you have. The box plot should have:

  • A line at 15 (Min),
  • A box starting at 20 (Q1) and ending at 29 (Q3),
  • A line in the box at 26 (Median),
  • A line at 32 (Max).

Please compare this summary with the given box plots to find the correct match.

tht does not match any of them can you try again

Let's carefully reevaluate the dataset and the steps for calculating the five-number summary.

The dataset is:
15, 20, 20, 25, 26, 28, 28, 30, 32

  1. Minimum:

    • Minimum (Min) = 15

  2. Maximum:

    • Maximum (Max) = 32

  3. Median (Q2):

    • The median is the middle value. There are 9 values in the dataset, so the median is the 5th value.
    • Median (Q2) = 26

  4. First Quartile (Q1):

    • Q1 is the median of the first half of the data. The first half consists of: 15, 20, 20, 25 (the first four values).
    • The median of (15, 20, 20, 25) is the average of 20 and 20, which is:
      \(Q1 = 20\)

  5. Third Quartile (Q3):

    • Q3 is the median of the second half of the data. The second half consists of: 28, 28, 30, 32 (the last four values).
    • The median of (28, 28, 30, 32) is the average of 28 and 30, which is:
      \(Q3 = \frac{28 + 30}{2} = 29\)

Now we summarize the five-number summary:

  • Minimum (Min) = 15
  • Q1 = 20
  • Median (Q2) = 26
  • Q3 = 29
  • Maximum (Max) = 32

Constructing the Box Plot

  • The box will start at \(20\) and end at \(29\) (Q1 to Q3).
  • Inside the box, there should be a line at \(26\) (the median).
  • The ends of the whiskers will go to the minimum \(15\) and the maximum \(32\).

Summary:

  • Q1 = 20
  • Median = 26
  • Q3 = 29

With these points, check the box plots again:

  • The box should cover from \(20\) to \(29\) with a line at \(26\).
  • The whiskers should extend to \(15\) and \(32\).

If you have any specific box plots to compare, please provide the details, and I can help you identify which one matches the summary above.