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The director of a local summer camp is interested in the number of hours kids spend on screens each week. He surveys a group of 15 kids at his camp and asks them how many hours they spent on screens last week. A list of his results follows. {0,7,8,8,10,11,14,15,17,17.5,18,18,18,20,30} The director realizes he forgot to include the data value “15” in his dataset. Calculate the interquartile range of the original dataset and the interquartile range of the new dataset after “15” is added. (1 point) The interquartile range of the original dataset is hours. The interquartile range of the new dataset after “15" is added is hours.

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To calculate the interquartile range (IQR) of the original dataset and the new dataset after adding "15," we need to follow these steps:

  1. Original Dataset: {0, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 18, 20, 30}

  2. Sort the Data: (already sorted in this case)

  3. Calculate Q1 and Q3 of the Original Dataset:

    • The original dataset has 15 values.

    • Q1 (the first quartile) is the median of the first half of the data:

      • First half: {0, 7, 8, 8, 10, 11, 14} (7 values)
      • Median of the first half (Q1) is the 4th number: 8.

    • To find Q3 (the third quartile), we take the median of the second half of the data:

      • Second half: {15, 17, 17.5, 18, 18, 18, 20, 30} (8 values)
      • Median of the second half (Q3) is the average of the 4th and 5th numbers:
      • (18 + 18) / 2 = 18.

  4. Interquartile Range (IQR) of the Original Dataset:

    • IQR = Q3 - Q1 = 18 - 8 = 10 hours.

Now we add the missing data value, "15", to the dataset.

  1. New Dataset: {0, 7, 8, 8, 10, 11, 14, 15, 15, 17, 17.5, 18, 18, 18, 20, 30}

  2. Sort the New Data: (it remains sorted)

  3. Calculate Q1 and Q3 of the New Dataset:

    • The new dataset has 16 values.

    • Q1 is the median of the first half:

      • First half: {0, 7, 8, 8, 10, 11, 14, 15} (8 values)
      • Median of the first half (Q1) is the average of the 4th and 5th numbers:
      • (8 + 10) / 2 = 9.

    • To find Q3, we take the median of the second half:

      • Second half: {15, 17, 17.5, 18, 18, 18, 20, 30} (8 values)
      • Median of the second half (Q3) is the average of the 4th and 5th numbers:
      • (18 + 18) / 2 = 18.

  4. Interquartile Range (IQR) of the New Dataset:

    • IQR = Q3 - Q1 = 18 - 9 = 9 hours.

Final Results:

  • The interquartile range of the original dataset is 10 hours.
  • The interquartile range of the new dataset after “15" is added is 9 hours.