Final answer:
The minimum value is 56, the first quartile (Q1) is 72, the median is 81, the third quartile (Q3) is 87, the maximum value is 98, and the width of the interquartile range (IQR) is 15.
Step-by-step explanation:
Calculating Minimum, Maximum, and Quartiles
To determine the minimum, maximum, and quartile values for a set of numbers, you should first arrange the numbers in order from smallest to largest. Then, you can calculate each required measure. For this set of numbers {90, 56, 75, 87, 98, 69, 72, 74, 83, 81, 81}, once they are arranged, they will look like this: 56, 69, 72, 74, 75, 81, 81, 83, 87, 90, 98.
a. The minimum value is the smallest number in the dataset, so it is 56.
b. The first quartile (Q1) is the median of the lower half of the dataset. In this case, that is 72.
c. The median or second quartile (Q2) is the middle value of the dataset, which is 81.
d. The third quartile (Q3) is the median of the upper half of the dataset, which is 87.
e. The maximum value is the largest number in the dataset, so it is 98.
f. The width of IQR (Interquartile Range) is the difference between Q3 and Q1, which is 87 - 72 = 15.