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Use the table to answer the question. Number of Siblings Number of 6th Graders 0 3 1 12 2 5 3 2 4 0 5 2 Kaylen wants to know how many siblings 6th graders have. She surveys the 6th graders on her soccer team. Her results are given in the table. She calculates that the interquartile range for number of siblings is 1. She then realizes that she counted one data value twice by accident. She needs to remove one of the “0 siblings” values from the table. Determine how removing a “0” from the dataset will impact the interquartile range. (1 point) Responses The new interquartile range is 1. The interquartile range stayed the same. The new interquartile range is 1. The interquartile range stayed the same. The new interquartile range is 0.5. The interquartile range decreased. The new interquartile range is 0.5. The interquartile range decreased. The new interquartile range is 6.5. The interquartile range increased. The new interquartile range is 6.5. The interquartile range increased. The new interquartile range is 1.5. The interquartile range increased.

1 answer

To determine how removing one "0 siblings" value from the dataset impacts the interquartile range (IQR), we first need to list the number of siblings for all the 6th graders based on the given table:

  • 0 siblings: 2 (since we remove 1, we'll have 1 left)
  • 1 sibling: 12
  • 2 siblings: 5
  • 3 siblings: 2
  • 4 siblings: 0
  • 5 siblings: 2

After surveying, we originally have this dataset:

  • 0, 0 (initially counted as two 0's)
  • 1 (12 times)
  • 2 (5 times)
  • 3 (2 times)
  • 5 (2 times)

So the complete original list of values is:

0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 5, 5

This gives us the data points:

Original dataset:
0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 5, 5

Now, if we remove one "0", the new dataset will be:

New dataset:
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 5, 5

Next, we will determine the IQR for both datasets.

To find the Quartiles:

  1. Original Dataset: (22 items)

    • Q1 is the median of the first half (11 values): 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1
    • Q1 = 1 (the average of the 6th and 7th values, which are both 1)
    • Q3 is the median of the second half (11 values): 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 5, 5
    • Q3 = 2 (the average of 6th and 7th values which are 2 and 2)

    IQR = Q3 - Q1 = 2 - 1 = 1

  2. New Dataset: (21 items)

    • Q1 is the median of the first half (10 values) now: 0, 1, 1, 1, 1, 1, 1, 1, 1, 1
    • Q1 = 1 (the average of the 5th and 6th values, which are both 1)
    • Q3 is the median of the second half (10 values): 1, 1, 1, 1, 2, 2, 2, 2, 3, 5
    • Q3 = 2 (the average of the 5th and 6th values, which are 2 and 2)

    IQR = Q3 - Q1 = 2 - 1 = 1

Conclusion:

Since the IQR remains at 1 for both the original dataset and the new dataset after removing one "0 siblings" value, the response is:

The interquartile range stayed the same.