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Answer the statistical measures and create a box and whiskers plot for the following set of data., On this question page, you will first be asked to fill in statistical measures, then create a box plot. Once you make adjustments to the box plot, the answer area will appear and you will be able to submit your answers.

8, comma, 9, comma, 9, comma, 11, comma, 11, comma, 14, comma, 15, comma, 15, comma, 16, comma, 18, comma, 18
8,9,9,11,11,14,15,15,16,18,18
Min:
Q1:
Med:
Q3:
Max:

1 answer

To find the statistical measures (minimum, first quartile Q1, median, third quartile Q3, and maximum) for the given data set \(8, 9, 9, 11, 11, 14, 15, 15, 16, 18, 18\), we first need to sort the data (but it's already sorted here) and then identify the required measures.

Statistical Measures:

  1. Minimum (Min): The smallest value in the dataset.

    • Min: \(8\)

  2. Maximum (Max): The largest value in the dataset.

    • Max: \(18\)

  3. Median: The middle value of the dataset.

    • Since there are 11 values (odd number), the median is the value at position \((11 + 1) / 2 = 6\).
    • Median: \(14\)

  4. First Quartile (Q1): The median of the first half of the data (values below the overall median).

    • The first half is \(8, 9, 9, 11, 11\) (5 values).
    • Q1: The median of this array is the 3rd value: \(9\).

  5. Third Quartile (Q3): The median of the second half of the data (values above the overall median).

    • The second half is \(15, 15, 16, 18, 18\) (5 values).
    • Q3: The median of this array is the 3rd value: \(16\).

Summarized Measures:

  • Min: \(8\)
  • Q1: \(9\)
  • Med (Median): \(14\)
  • Q3: \(16\)
  • Max: \(18\)

Box and Whiskers Plot:

Now, you would plot these points on a box-and-whiskers plot with the following information:

  • Draw a box from Q1 (\(9\)) to Q3 (\(16\)).
  • Inside the box, place a line at the median (\(14\)).
  • Extend "whiskers" from the box to the minimum (\(8\)) and maximum (\(18\)).

The box-and-whiskers plot visually represents these statistical measures, capturing the spread and central tendency of the data.

Feel free to adjust the plot based on this information!