Final answer:
To determine the minimum, maximum and quartile values of the set {-9, -8, -5, -3, -2, 0, 2, 3, 5, 8, 9}, we arrange the data in ascending order and identify -9 as the minimum value, 9 as the maximum value, -5 as the first quartile, 0 as the median, 5 as the third quartile, and the interquartile range (IQR) as 10.
Step-by-step explanation:
To determine the minimum, maximum, and quartile values for the given data set {8, 9, 3, 2, 5, -8, -9, -3, -2, -5, 0}, we first need to arrange the data in ascending order. The ordered data set is {-9, -8, -5, -3, -2, 0, 2, 3, 5, 8, 9}. Now we can clearly see and identify the minimum and maximum values.
Minimum and Maximum Values
The minimum value is the smallest number in the set, which is -9, and the maximum value is the largest number in the set, which is 9.
Quartiles
The median (or second quartile Q2) is the middle value of the ordered set. Since we have 11 data points, the median is the 6th value, which is 0. The first quartile (Q1) is the median of the lower half of the data not including the median itself. In this case, it will be the median of the first five numbers {-9, -8, -5, -3, -2}, which is -5. The third quartile (Q3) is the median of the upper half of the data, which is the median of these five numbers {2, 3, 5, 8, 9}, which is 5. The IQR (interquartile range) is calculated as Q3 - Q1, which in this case is 5 - (-5) = 10.
Box Plot
The five number summary necessary to create a box plot for this data includes the minimum value, Q1, median (Q2), Q3, and maximum value. Once you have these five values, you can easily construct a box plot to graphically represent the data distribution.