Final answer:
The minimum value is 56, the first quartile is 73, the median is 81, the third quartile is 88.5, and the maximum value is 98. The width of the IQR is 15.5.
Step-by-step explanation:
To determine the minimum, maximum, and quartile values, you must first arrange the data in ascending order: 56, 69, 72, 74, 75, 81, 81, 83, 87, 90, 98. With the data in order, you can then proceed to find the various measures.
The minimum value is the smallest number in the set, which is 56.
The maximum value is the largest number in the set, which is 98.
To determine the quartiles, the data set is split into four equal parts. The second quartile or median is the middle value, which is 81 since it is the sixth value in the ordered list (from either direction).
The first quartile (Q1) is the median of the lower half of the data set (excluding the overall median if the number of data points is odd), which, in this case, is the average of 72 and 74, yielding 73.
The third quartile (Q3) is the median of the upper half of the data set, which is the average of 87 and 90, yielding 88.5.
The width of the IQR is the difference between the third and first quartiles, which is 88.5 - 73 = 15.5.