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)
The median of the original dataset is
hours. The median of the new dataset after “5" is added is
hours.
To find the median, we first need to put the data values in order from least to greatest:
{0, 5, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 20, 30}
There are 15 data values, so the median will be the middle value, which is the 8th value in this case.
Median of the original dataset: 14 hours
Now we add the missing data value "5" to the dataset:
{0, 5, 5, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 20, 30}
Since there are now 16 data values, the median will be the average of the 8th and 9th values.
Median of the new dataset: (10 + 11) / 2 = 10.5 hours
Therefore, the median of the original dataset is 14 hours, and the median of the new dataset after "5" is added is 10.5 hours.
wrong
My apologies for the error in my previous response.
First, let's find the median of the original dataset:
{0, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 20, 30}
Since there are 14 data values, the median will be the average of the middle two values, which are the 7th and 8th values in this case:
Median of the original dataset: (14 + 15) / 2 = 14.5 hours
Now, we add the missing data value "5" to the original dataset:
{0, 5, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 20, 30}
Since there are 15 data values,
Median of the new dataset: 11 hours
Therefore, the correct median of the original dataset is 14.5 hours, and the correct median of the new dataset after "5" is added is 11 hours.