Question

Determine the minimum, maximum, and quartile values. Remember, the first step is to put the values in order from least to greatest.

{8,9,3,2,5,-8,-9,-3,-2,-5,0}

Answer 1

To calculate the minimum, maximum, and quartiles, organize the data in ascending order. The minimum is -9 and the maximum is 9. The first quartile (Q1) is -5, the median (Q2) is 2, and the third quartile (Q3) is 6.5.

Step-by-step explanation:

Calculating Minimum, Maximum, and Quartiles

To determine the minimum value, maximum value, and quartiles, you need to organize the given data set in ascending order: {-9, -8, -5, -3, -2, 0, 2, 3, 5, 8, 9}. Now we can easily identify the minimum and maximum values and calculate the quartiles.

1. The minimum value is the smallest number in the data set, which is -9.
2. The maximum value is the largest number in the data set, which is 9.
3. To find the median (Q2), we look for the middle number. In this case, with 11 numbers, the median is the 6th number when ordered, which is 2.
4. The lower half of the set (not including the median) is {-9, -8, -5, -3, -2}. The first quartile (Q1) is the median of the lower half: -5.
5. The upper half of the set (not including the median) is {3, 5, 8, 9}. The third quartile (Q3) is the median of the upper half, which is 6.5, the average of 5 and 8.
6. The width of the IQR (Interquartile Range) is the difference between the third and first quartile, which is 6.5 - (-5) or 11.5.

A box plot can be constructed using these values, with the quartiles defining the edges of the box and the whiskers extending to the minimum and maximum data values.