To find the interquartile range (IQR) of the original dataset, we first need to find the lower and upper quartiles.
Original dataset: 4, 3, 1, 1, 3, 7, 2, 1
Step 1: Organize the data in ascending order:
1, 1, 1, 2, 3, 3, 4, 7
Step 2: Calculate the median of the entire dataset:
Median = (3 + 3) / 2 = 3
Step 3: Split the dataset into two halves, the first half (lower) and the second half (upper).
Lower half: 1, 1, 1, 2
Upper half: 3, 3, 4, 7
Step 4: Calculate the median of each half. These are the lower quartile (Q1) and upper quartile (Q3).
Q1 = (1 + 1) / 2 = 1
Q3 = (3 + 4) / 2 = 3.5
Now, we can calculate the interquartile range (IQR):
IQR = Q3 - Q1
IQR = 3.5 - 1
IQR = 2.5
The interquartile range (IQR) of the original dataset is 2.5.
Next, we will calculate the interquartile range (IQR) of the new dataset with Michael's data point added.
New dataset: 4, 3, 1, 1, 3, 7, 2, 1, 4
Step 1: Organize the data in ascending order:
1, 1, 1, 2, 3, 3, 4, 4, 7
Step 2: Calculate the median of the entire dataset:
Median = 3
Step 3: Split the dataset into two halves, the first half (lower) and the second half (upper).
Lower half: 1, 1, 1, 2
Upper half: 3, 3, 4, 4, 7
Step 4: Calculate the median of each half. These are the lower quartile (Q1) and upper quartile (Q3).
Q1 = (1 + 1) / 2 = 1
Q3 = (3 + 4) / 2 = 3.5
Now, we can calculate the interquartile range (IQR) of the new dataset:
IQR = Q3 - Q1
IQR = 3.5 - 1
IQR = 2.5
The interquartile range (IQR) of the new dataset with Michael's data point added is also 2.5.
Pairs of shoes: 2 3 4 5 6 7 8 10
6th graders: 4 3 1 1 3 7 2 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.
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