To find the IQR (Interquartile Range), you need to find the values of the first quartile (Q1) and the third quartile (Q3) of the given set of numbers.
First, we need to arrange the given numbers in ascending order:
144, 194, 279, 406, 414, 464, 594, 879
Next, we determine the median (Q2) of the set. Since there are 8 numbers, the median is the mean of the two middle values, which are 406 and 414.
(Q2) = (406 + 414) / 2 = 820 / 2 = 410
Now, we need to determine the median of the lower half of the set, i.e., the quartile Q1. Q1 is the median of the numbers on the left side of the median (Q2). In this case, the numbers are 144, 194, 279, and 406.
(Q1) = (194 + 279) / 2 = 473 / 2 = 236.5
Lastly, we need to determine the median of the upper half of the set, i.e., the quartile Q3. Q3 is the median of the numbers on the right side of the median (Q2). In this case, the numbers are 414, 464, 594, and 879.
(Q3) = (464 + 594) / 2 = 1058 / 2 = 529
Finally, the IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 529 - 236.5 = 292.5
Therefore, the Interquartile Range (IQR) of the given set is 292.5.