In the data set below, what is the interquartile range?
1 3 4 4 5 6 7
To find the interquartile range, first we need to find the first and third quartiles.
First, we need to find the median of the data set:
1 3 4 4 5 6 7
The median is 4.
Since the data set has an odd number of values, we exclude the median and split the data set into two halves:
1 3 4
5 6 7
Next, we find the median of each half:
First half: median is 3
Second half: median is 6
The first quartile (Q1) is 3 and the third quartile (Q3) is 6.
Now, we calculate the interquartile range (IQR) by subtracting Q1 from Q3:
6 - 3 = 3
Therefore, the interquartile range is 3.