To calculate the interquartile range (IQR), we first need to find the first quartile (Q1) and third quartile (Q3) of the dataset.
Original dataset:
{0,7,8,8,10,11,14,15,17,17.5,18,18,18,20,30}
After sorting the dataset in ascending order:
0, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 18, 20, 30
Q1 = 8.5
Q3 = 18
IQR = Q3 - Q1 = 18 - 8.5 = 9.5
Now let's calculate the IQR of the new dataset after adding 15:
{0,7,8,8,10,11,14,15,15,17,17.5,18,18,18,20,30}
After sorting the dataset in ascending order:
0, 7, 8, 8, 10, 11, 14, 15, 15, 17, 17.5, 18, 18, 18, 20, 30
Q1 = 10
Q3 = 18
IQR = Q3 - Q1 = 18 - 10 = 8
Therefore, the interquartile range of the original dataset is 9.5 hours and the interquartile range of the new dataset after adding "15" is 8 hours.
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.
{0,7,8,8,10,11,14,15,17,17.5,18,18,18,20,30}
The director realizes he forgot to include the data value “15” in his dataset. Calculate the interquartile range of the original dataset and the interquartile range of the new dataset after “15” is added.
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