In the data set below, what is the interquartile range?
85,49,83,88,65,29
To find the interquartile range (IQR), first we need to find the median of the data set.
29, 49, 65, 83, 85, 88
The median is the middle value, which is 76.
Next, we need to find the median of the lower half of the data set (values below 76).
29, 49, 65
The median of this lower half is 49.
Finally, we need to find the median of the upper half of the data set (values above 76).
83, 85, 88
The median of this upper half is 85.
To find the IQR, we subtract the lower quartile (Q1) from the upper quartile (Q3).
Q1 = 49 Q3 = 85
IQR = Q3 - Q1 = 85 - 49 = 36
Therefore, the interquartile range for this data set is 36.