Answer
The IQR of the data set is 368.
Explanation
To find the interquartile range, you first need to find the median of the data set. Then, you find the median of the median and subtract them. This might be a little confusing but I'll walk through everything.
First, put the data set in order from least to greatest; 21 78 90 111 381 456 676. Find the median. The median of this data set is 111, since it is the middle number when the data set is ordered from least to greatest.
To find the Q1 and Q3 of the set, you have to find the median of the median.
The set right now is 21 78 90 111 381 456 676. Remove the 111 (if there were an even amount of numbers in the set, you wouldn't remove the 111 and you would just split the data set in half). Now you have two sets: 21 78 90 and 381 456 676. The median of the first set is 78 (this is the Q1) and the median of the second set is 456 (this is the Q3).
To find the interquartile range, subtract the Q1 from the Q3. 456-78=368.
