15, 12, 11, 16, 17, 12, 11, 17, 12
What is the spread (range) and the interquartile range (IQR) of this data set?
To find the range, we need to subtract the smallest value from the largest value.
The smallest value in the data set is 11, and the largest value is 17.
Therefore, the range is 17 - 11 = 6.
To find the interquartile range (IQR), we first need to find the lower quartile (Q1) and the upper quartile (Q3).
To find Q1, we need to find the median of the lower half of the data.
The lower half of the data is: 11, 11, 12, 12
To find the median of this set, we take the average of the two middle numbers: (11 + 12) / 2 = 11.5
So, Q1 = 11.5
To find Q3, we need to find the median of the upper half of the data.
The upper half of the data is: 15,16,17,17
To find the median of this set, we take the average of the two middle numbers: (16 + 17) / 2 = 16.5
So, Q3 = 16.5
Finally, the IQR is found by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 16.5 - 11.5 = 5