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Aziz wonders how many pieces of pizza people tend to eat at a pizza party. He surveys 11 people at the end of a pizza party and asks them how many pieces of pizza they ate. A list of his results follows. Aziz uses his results to calculate that the range for number of pieces of pizza eaten is 6, and the interquartile range is 4. Number of Pieces of Pizza Eaten: 6, 2, 1, 2, 4, 5, 2, 2, 4, 6, 7 After calculating the range and the interquartile range, Aziz realizes he forgot to include himself! He ate 3 pieces of pizza. Determine the range and interquartile range after a “3” is added to the dataset. Describe how adding a “3” to the dataset impacts the range and the interquartile range. (1 point) Responses The range is now 7, but the interquartile range is still 4. The range increased slightly, but the interquartile range stayed the same. The range is now 7, but the interquartile range is still 4. The range increased slightly, but the interquartile range stayed the same. The range is still 6, but the interquartile range is now 3.5. The range stayed the same, but the interquartile range changed slightly. The range is still 6, but the interquartile range is now 3.5. The range stayed the same, but the interquartile range changed slightly. The range is now 7, and the interquartile range is now 3.5. Both the range and the interquartile range changed slightly. The range is now 7, and the interquartile range is now 3.5. Both the range and the interquartile range changed slightly. The range is still 6, and the interquartile range is still 4. Both the range and the interquartile range stayed the same. The range is still 6, and the interquartile range is still 4. Both the range and the interquartile range stayed the same.

1 answer

To determine the impact of adding Aziz's pizza consumption (3 pieces) to the dataset, let's first summarize the data and recalculate the required statistics.

Initial dataset (before including Aziz):

Number of Pieces of Pizza Eaten: 6, 2, 1, 2, 4, 5, 2, 2, 4, 6, 7

Sorted order of initial dataset: 1, 2, 2, 2, 2, 4, 4, 5, 6, 6, 7

Calculating the range:

  • Minimum value = 1
  • Maximum value = 7
  • Range = Max - Min = 7 - 1 = 6 (as provided)

Calculating Q1 and Q3 for the interquartile range:

  • Q1 is the median of the first half: (1, 2, 2, 2, 2) → Median = 2
  • Q3 is the median of the second half: (4, 4, 5, 6, 6, 7) → Median = 5
  • Interquartile Range (IQR) = Q3 - Q1 = 5 - 2 = 3 (This contradicts the original IQR of 4, which seems to be miscalculated. It was stated as 4, but based on values, it appears to be 3.)

Now, by including Aziz's consumption (3 pieces), the new dataset becomes: 1, 2, 2, 2, 2, 3, 4, 4, 5, 6, 6, 7

Re-sorting the new dataset: 1, 2, 2, 2, 2, 3, 4, 4, 5, 6, 6, 7

Calculating the new range:

  • Minimum value = 1
  • Maximum value = 7
  • New Range = 7 - 1 = 6 (the range stays the same)

Calculating Q1 and Q3 for the new interquartile range:

  • For the lower half (1, 2, 2, 2, 2), Q1 = 2 (remains same).
  • For the upper half (3, 4, 4, 5, 6, 6, 7):
    • This needs averaging the middle values since we now have 12 total values. We basically need the 8th and 9th values; both are 4 and 5.
  • Q3 = (5 + 4) / 2 = 4.5

Thus, the new IQR = Q3 - Q1 = 4.5 - 2 = 2.5

Based on these calculations:

  • The new range is still 6, and the interquartile range is now 2.5 (which impacts the original assumption).

Final Summary of Results:

  • The range is still 6.
  • The interquartile range is now 2.5 (not 4 as initially listed).

Final Response:

  • The range is still 6, but the interquartile range is now different (2.5).
  • It shows that while extreme values define the range, the IQR can change when central values are added or modified.

The correct choice would fit within these interpretations, adjusting how one would summarize the slight changes in interquartile range based on included values.