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A meteorologist recorded the following temperatures: {71,74,81,78,67,69,64}

. Today's temperature is 67º. If today’s temperature is included in the dataset, how does it change the interquartile range?(1 point)
The interquartile range of the new dataset is
. It changed by

1 answer

To determine how today's temperature of 67º changes the interquartile range (IQR) of the dataset, we first need to calculate the IQR of the original dataset and then including today's temperature.

Original Dataset:

Original temperatures: {71, 74, 81, 78, 67, 69, 64}

  1. Sort the original dataset:

    • Sorted: {64, 67, 69, 71, 74, 78, 81}

  2. Find the quartiles:

    • Q1 (first quartile): Median of the first half {64, 67, 69} → Q1 = 67
    • Q3 (third quartile): Median of the second half {74, 78, 81} → Q3 = 78

  3. Calculate the IQR:

    • IQR = Q3 - Q1 = 78 - 67 = 11

New Dataset:

New temperatures including today's: {71, 74, 81, 78, 67, 69, 64, 67}

  1. Sort the new dataset:

    • Sorted: {64, 67, 67, 69, 71, 74, 78, 81}

  2. Find the quartiles:

    • Q1 (first quartile): Median of the first half {64, 67, 67, 69} → Q1 = (67 + 67) / 2 = 67
    • Q3 (third quartile): Median of the second half {71, 74, 78, 81} → Q3 = (74 + 78) / 2 = 76

  3. Calculate the IQR:

    • IQR = Q3 - Q1 = 76 - 67 = 9

Change in IQR:

  • Original IQR = 11
  • New IQR = 9

Change in IQR = New IQR - Original IQR = 9 - 11 = -2

Summary

  • The interquartile range of the new dataset is 9.
  • It changed by -2.