What is the interquartile range of the following data set?
78, 90, 456, 676, 111, 381, 21
First, we need to order the data set: 21, 78, 90, 111, 381, 456, 676
Then, we find the quartiles:
The first quartile (Q1) is the median of the lower half of the data set, which is 21, 78, 90. The median of this set is 78.
The third quartile (Q3) is the median of the upper half of the data set, which is 381, 456, 676. The median of this set is 456.
Finally, we calculate the interquartile range by subtracting Q1 from Q3: 456 - 78 = <<456-78=378>>378.
Therefore, the interquartile range of the data set is 378.