Answer:
37.5
Explanation:
To find the interquartile range (IQR) for a data set, we need to find the difference between the upper quartile (Q3) and the lower quartile (Q1).
To find Q1 and Q3, we first need to order the data set from lowest to highest:
25, 49, 50, 60, 60, 70, 70, 74, 81, 85, 89, 100
There are 12 data points in this set, so the median is the average of the sixth and seventh numbers:
median = (70 + 70)/2 = 70
To find Q1, we take the median of the first half of the data set (the numbers to the left of the median). There are six numbers in the first half, so the median is the average of the third and fourth numbers:
Q1 = (49 + 50)/2 = 49.5
To find Q3, we take the median of the second half of the data set (the numbers to the right of the median). Again, there are six numbers in the second half, so the median is the average of the ninth and tenth numbers:
Q3 = (85 + 89)/2 = 87
Now we can find the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 87 - 49.5 = 37.5
Therefore, the interquartile range for the given data set is 37.5.