Use this data set for all problems in this practice: 15, 12, 11, 16, 17, 12, 11, 17, 12
What is the spread (range) and Interquartile Range (IQR) of this data set?
To find the range of a data set, we subtract the smallest value from the largest value.
In this case, the smallest value is 11 and the largest value is 17.
Therefore, the range of the data set is 17 - 11 = 6.
To find the interquartile range (IQR) of a data set, we first need to find the upper quartile (Q3) and the lower quartile (Q1).
To do this, we first need to find the median (Q2) of the data set.
Arranging the data set in ascending order, we have: 11, 11, 12, 12, 12, 15, 16, 17, 17.
The median (Q2) is the middle value, which is 12.
Next, we find the lower quartile (Q1), which is the median of the lower half of the data set.
The lower half is: 11, 11, 12, 12.
The median of this lower half is (11 + 12) / 2 = 11.5.
Finally, we find the upper quartile (Q3), which is the median of the upper half of the data set.
The upper half is: 15, 16, 17, 17.
The median of this upper half is (16 + 17) / 2 = 16.5.
Therefore, the interquartile range (IQR) is Q3 - Q1 = 16.5 - 11.5 = 5.