To find the IQR (Interquartile Range) of a set of data, we first need to find the median of the data set. The median is the middle value when the data set is arranged in order.
Arranging the given data set in order:
105 106 107 117 118 123 125 127 136
The median of this data set is the middle value, which is 123.
Next, we need to find the values of the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set.
The lower half of the data set is: 105 106 107 117 118
The upper half of the data set is: 123 125 127 136
Q1 is the median of the lower half of the data set, which is:
Q1 = (107 + 117)/2 = 112
Q3 is the median of the upper half of the data set, which is:
Q3 = (125 + 127)/2 = 126
Finally, we can calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 126 - 112 = 14
Therefore, the IQR of the given data set is 14.