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.
(1 point)
The interquartile range of the original dataset is
hours.
The interquartile range of the new dataset after “15" is added is
hours.
To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3) of the dataset.
First, let's find the quartiles of the original dataset:
Q1 = (n+1)/4 = 16/4 = 4th value = 8.5
Q3 = 3(n+1)/4 = 3*16/4 = 12th value = 18
Original dataset = {0, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 18, 20, 30}
Interquartile range of the original dataset = Q3 - Q1 = 18 - 8.5 = 9.5 hours
Now, let's add the forgotten data value "15" to the dataset:
New dataset = {0, 7, 8, 8, 10, 11, 14, 15, 15, 17, 17.5, 18, 18, 18, 20, 30}
Now, let's find the quartiles of the new dataset:
Q1 = (n+1)/4 = 17/4 = 4.25th value = (8 + 10)/2 = 9
Q3 = 3(n+1)/4 = 3*17/4 = 12.75th value = (17.5 + 18)/2 = 17.75
Interquartile range of the new dataset = Q3 - Q1 = 17.75 - 9 = 8.75 hours
Therefore, the interquartile range of the original dataset is 9.5 hours, and the interquartile range of the new dataset after "15" is added is 8.75 hours.