The director of a local summer camp is interested in the number of hours kids spend on screens each week. He surveys a group of 15 kids at his camp and asks them how many hours they spent on screens last week. A list of his results follows.
{0,7,8,8,10,11,14,15,17,17.5,18,18,20,30}
The director realizes he forgot to include the data value “5” in his dataset. Calculate the median of the original dataset and the median of the new dataset after “5” is added.
The median of the original dataset is hours. The median of the new dataset after “5" is added is ___ hours.
To find the median of a dataset, you first need to arrange the data in ascending order.
Original dataset: {0, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 20, 30}
After arranging in ascending order: {0, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 20, 30}
The total number of data points is 14, which is even. In this case, the median will be the average of the two middle numbers:
Median = (11 + 14) / 2 = 25 / 2 = 12.5 hours
Now, let's add the value of 5 to the dataset.
New dataset: {0, 5, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 20, 30}
After arranging in ascending order: {0, 5, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 20, 30}
The total number of data points is 15, which is odd. The median will be the middle number:
Median = 11 hours
Therefore, the median of the original dataset is 12.5 hours, and the median of the new dataset after "5" is added is 11 hours.