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Number of Siblings Number of 6th Graders 0 3 1 12 2 5 3 2 4 0 5 1 Kaylen wants to know the number of siblings 6th graders typically have. She surveys the 6th graders on her soccer team. Her results are given in the table. She calculates that the median 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 median. (1 point) Responses The new median is 1. The median stayed the same. The new median is 1. The median stayed the same. The new median is 1.5. The median increased. The new median is 1.5. The median increased. The new median is 3. The median increased. The new median is 3. The median increased. The new median is 5. The median increased.

1 answer

To determine how removing one "0" from the dataset affects the median, let's first understand the data in the table after confirming it's complete.

The original dataset of the number of siblings is as follows:

  • 0 siblings: 3 times (0, 0, 0)
  • 1 sibling: 12 times (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
  • 2 siblings: 5 times (2, 2, 2, 2, 2)
  • 3 siblings: 2 times (3, 3)
  • 4 siblings: 0 times
  • 5 siblings: 1 time (5)

Now if we list the data based on the counts, we get:

\[0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 5\]

This totals to 21 values.

To find the median of this group, we can find the 11th value (since there are 21 total numbers, the median is the middle number):

The 11th value in this sorted list is 1. Hence, the original median is indeed 1.

Next, we remove one instance of "0":

The new dataset will be:

\[0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 5\]

This adjusted list now contains 20 values.

To find the new median in this list, we need to average the 10th and 11th values (since there are now an even number of total values):

The 10th value is 1, and the 11th value is 1 as well.

So:

\[ \text{New median} = \frac{1 + 1}{2} = 1 \]

Thus, the new median remains 1 and does not change.

Final Answer: The new median is 1. The median stayed the same.