Answer:
The interquartile range for the data set is 35.5.
Step-by-step explanation:
To calculate the interquartile range for the data set, you must first arrange the numbers in increasing order:
241, 230, 201, 245, 209, 211, 242, 201, 204, 228, 242, 243
201, 201, 204, 209, 211, 228, 230, 241, 242, 242, 243, 245
Next, find the median of the data set:
201, 201, 204, 209, 211, 228, 230, 241, 242, 242, 243, 245
201, 204, 209, 211, 228, 230, 241, 242, 242, 243
204, 209, 211, 228, 230, 241, 242, 242
209, 211, 228, 230, 241, 242
211, 228, 230, 241
228, 230
Since there are two numbers left when calculating the median, the median is the average of the two numbers:
Average = [tex]\frac{sum of data}{number of values}[/tex]
A = [tex]\frac{228 + 230}{2}[/tex]
A = [tex]\frac{458}{2}[/tex]
A = 229
This means that Median = 229
Now, calculate the median of both the lower and upper half of the data:
201, 201, 204, 209, 211, 228 | 230, 241, 242, 242, 243, 245
201, 204, 209, 211 | 241, 242, 242, 243
204, 209 | 242, 242
206.5 | 242
Finally, the interquartile range is the difference between these two upper and lower medians:
242 - 206.5
IQR = 35.5
