Use the table to answer the question.
Number of Pairs of Shoes Number of 6th Graders
2 5
3 6
4 1
5 1
6 4
7 7
8 2
10 1
Michael wants to know how many pairs of shoes 6th graders typically 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.
Calculate the median of the original dataset and the median of the new dataset with the data point for Michael’s 4 pairs of shoes added.
(1 point)
The median of the original dataset is
. The median of the new dataset after another “4” is added is
.
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To calculate the median of the original dataset, we first need to rearrange the data in ascending order:
1, 1, 2, 3, 4, 5, 6, 7
Since the dataset has 8 data points, the median is the average of the 4th and 5th data points, which are 3 and 4. So, the median of the original dataset is (3 + 4) / 2 = 3.5.
Now, let's add Michael's data point of 4 to the dataset:
1, 1, 2, 3, 4, 4, 5, 6, 7
Since the dataset now has 9 data points, the median is the middle data point, which is 4. So, the median of the new dataset after adding Michael's data point is 4.