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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 find the interquartile range (IQR) of the dataset before and after including today's temperature of 67º, we need to first calculate the IQR of the original dataset and then the new dataset that includes the temperature.

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

  1. Sort the original dataset: \[ {64, 67, 69, 71, 74, 78, 81} \]

  2. Find the quartiles:

    • The median (Q2) is the middle value: 71
    • The lower quartile (Q1) is the median of the first half: {64, 67, 69}
      • Q1 = 67
    • The upper quartile (Q3) is the median of the second half: {74, 78, 81}
      • Q3 = 78

  3. Calculate IQR for the original dataset: \[ \text{IQR} = Q3 - Q1 = 78 - 67 = 11 \]

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

  1. Sort the new dataset: \[ {64, 67, 67, 69, 71, 74, 78, 81} \]

  2. Find the quartiles:

    • The median (Q2) is the average of the two middle values:
      • Median = (69 + 71)/2 = 70
    • The lower quartile (Q1) is the median of the first half: {64, 67, 67, 69}
      • Q1 = (67 + 67)/2 = 67
    • The upper quartile (Q3) is the median of the second half: {71, 74, 78, 81}
      • Q3 = (74 + 78)/2 = 76

  3. Calculate IQR for the new dataset: \[ \text{IQR} = Q3 - Q1 = 76 - 67 = 9 \]

Comparison:

  • Original IQR: 11
  • New IQR: 9

Changes:

  • The interquartile range of the new dataset is 9. It changed by \(11 - 9 = 2\).

So the final answers are:

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