To find the interquartile range (IQR), we first need to find the first quartile (Q1) and the third quartile (Q3).
Original dataset:
1. Sort the dataset in ascending order:
1, 1, 2, 2, 3, 3, 3, 4, 7, 7
2. Find the median of the dataset. Since the dataset has an even number of values, the median is the average of the two middle numbers:
(3 + 3) / 2 = 3
3. Q1 is the median of the lower half of the dataset:
(1 + 1 + 2 + 2) / 4 = 1.5
4. Q3 is the median of the upper half of the dataset:
(4 + 7 + 7) / 3 = 6
IQR = Q3 - Q1
IQR = 6 - 1.5
IQR = 4.5
New dataset with Michael's data added:
1, 1, 2, 2, 3, 3, 3, 4, 4, 7, 7
Finding Q1 and Q3 for the new dataset:
Q1 = (1 + 1 + 2 + 2) / 4 = 1.5
Q3 = (4 + 7 + 7) / 3 = 6
IQR = Q3 - Q1
IQR = 6 - 1.5
IQR = 4.5
Therefore, the interquartile range of the original dataset and the new dataset with Michael's data added is the same at 4.5.
Use the table to answer the question. Number of Pairs of Shoes Number of 6th Graders 2 4 3 3 4 1 5 1 6 3 7 7 8 2 10 1 Michael wants to know how many pairs of shoes 6th graders own. He surveys the 6th graders at his summer camp. His results are given in the table. After Michael creates the table, he realizes that he forgot to include himself. Michael owns 4 pairs of shoes. Determine the interquartile range (IQR) of the original dataset and the interquartile range of the new dataset with the data point for Michael’s 4 pairs of shoes added. (1 point) The interquartile range of the original dataset is . The interquartile range of the new dataset after another “4” is added is .
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