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.(1 point)
To calculate the median of the original dataset, we first need to arrange the data in ascending order:
{0, 5, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 20, 30}
The original dataset has 15 data points, so the median is the middle value. Since the dataset has an odd number of values, the median is the middle value, which is the 8th value in the dataset:
Median = 14
Now, let's find the median of the new dataset with the additional value of 5:
{0, 5, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 20, 30}
The dataset now has 16 data points, so the median is the average of the two middle values. The middle two values are the 8th and 9th values in the dataset:
Median = (14 + 15) / 2 = 14.5
Therefore, the median of the original dataset is 14 and the median of the new dataset after adding "5" is 14.5.