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.
After adding Aziz's data point (3 pieces of pizza) to the dataset, the new list becomes:
6, 2, 1, 2, 4, 5, 2, 2, 4, 6, 7, 3
To calculate the new range, we need to find the difference between the maximum and minimum values in the dataset:
Range = 7 - 1 = 6
To calculate the new interquartile range, we first need to find the first and third quartiles. The dataset is now in ascending order: 1, 2, 2, 2, 2, 3, 4, 4, 5, 6, 6, 7.
The median is the middle value of the dataset, which is between 3 and 4, so the first quartile Q1 is the median of the first half of the dataset: Q1 = (2 + 2) / 2 = 2
The median of the second half of the dataset is the third quartile Q3: Q3 = (5 + 6) / 2 = 5.5
Interquartile Range = Q3 - Q1 = 5.5 - 2 = 3.5
By adding Aziz's data point of 3 pieces of pizza to the dataset, both the range and the interquartile range increased. The range increased from 6 to 6, and the interquartile range increased from 4 to 3.5. This suggests that Aziz's data point had a greater impact on the interquartile range than on the range.
whats the range now?
After adding Aziz's data point of 3 pieces of pizza to the dataset, the new list becomes:
1, 2, 2, 2, 2, 3, 4, 4, 5, 6, 6, 7
To calculate the new range, we need to find the difference between the maximum and minimum values in the dataset:
Range = 7 - 1 = 6
So, the range remains 6 even after adding Aziz's data point.
whats the interquartile
After adding Aziz's data point of 3 pieces of pizza to the dataset, the first quartile Q1 is 2 and the third quartile Q3 is 5.5.
To calculate the interquartile range:
Interquartile Range = Q3 - Q1 = 5.5 - 2 = 3.5
Therefore, the interquartile range after adding Aziz's data point is 3.5.