To find the interquartile range, we first need to find the first and third quartiles of the dataset.
Original dataset: {0,7,8,8,10,11,14,15,17,17.5,18,18,18,20,30}
Step 1: Arrange the data in ascending order.
0, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 18, 20, 30
Step 2: Find the median (Q2) of the data.
Median = (15th term + 16th term) / 2
Median = (17 + 17.5) / 2
Median = 17.25
Step 3: Find the first quartile (Q1). This is the median of the lower half of the data.
Q1 = Median of (0, 7, 8, 8, 10, 11, 14, 15)
Q1 = (8 + 10) / 2
Q1 = 9
Step 4: Find the third quartile (Q3). This is the median of the upper half of the data.
Q3 = Median of (17.5, 18, 18, 18, 20, 30)
Q3 = (18 + 18) / 2
Q3 = 18
Now, we can calculate the interquartile range (IQR) for the original dataset.
IQR = Q3 - Q1
IQR = 18 - 9
IQR = 9 hours
New dataset after adding 15: {0,7,8,8,10,11,14,15,15 (new), 17,17.5,18,18,18,20,30}
The new median (Q2) remains the same at 17.25.
Now, we recalculate Q1 and Q3 for the new dataset.
New Q1 = Median of (0, 7, 8, 8, 10, 11, 14, 15, 15)
New Q1 = (10 + 11) / 2
New Q1 = 10.5
New Q3 = Median of (17, 17.5, 18, 18, 18, 20, 30)
New Q3 = (18 + 18) / 2
New Q3 = 18
Now, we calculate the new interquartile range (IQR) for the new dataset.
New IQR = Q3 - Q1
New IQR = 18 - 10.5
New IQR = 7.5 hours
Therefore, the interquartile range of the original dataset is 9 hours, and the interquartile range of the new dataset after adding "15" is 7.5 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. (1 point) The interquartile range of the original dataset is __ hours. The interquartile range of the new dataset after “15" is added is __ hours.
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