Use the table to answer the question.
Number of Pairs of Shoes: 2, 3, 4, 5, 6, 7, 8, 10
Number of 6th Graders: 5, 6, 1, 1, 4, 7, 2, 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.
The median of the original dataset is ----. The median of the new dataset after another “4” is added is ---- .
o find the median, we first need to arrange the data in ascending order and then find the middle value. If there is an even number of data points, the median is the average of the two middle values.
The original dataset is: 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 10.
There are 33 data points, so the median is the 17th value, which is 6.
The median of the original dataset is 6.
Now, let's add Michael's 4 pairs of shoes to the dataset: 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 10.
Now, We cross out the numbers and we are left with 5 and 6. We add them and divide it by 2
6+5=11 11/2=5.5
The median of the new dataset after another "4" is added is 5.5.
Thank you for the correction. The correct median of the new dataset after adding Michael's 4 pairs of shoes is 5.5, not 4 as previously calculated.
To find the median of a dataset, we must first rearrange the data in either ascending or descending order.
Original dataset: 1, 1, 1, 2, 4, 5, 6, 7
New dataset with Michael's 4 pairs of shoes added: 1, 1, 1, 2, 4, 4, 5, 6, 7
For datasets with an odd number of values, the median is simply the middle value when the data is sorted. For datasets with an even number of values, the median is the average of the two middle values when the data is sorted.
Original dataset median: (2 + 4) / 2 = 3
New dataset median: 4
Therefore, the median of the original dataset is 3 and the median of the new dataset after Michael's 4 pairs of shoes is added is 4.