Question

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

{2,3,7,1,4,5,6,10,9,4,6,7}

Answer 1

To find the minimum, maximum, and quartiles for the given set, arrange the values in order: 1, 2, 3, 4, 4, 5, 6, 6, 7, 7, 9, 10. Then, identify the minimum (1), first quartile (4), median (5.5), third quartile (7), and maximum (10) values. The width of IQR is 3.

Step-by-step explanation:

Calculating Minimum, Maximum, and Quartile Values

To calculate the minimum, maximum, and quartile values of a data set, first arrange the numbers in ascending order. Using the sorted data, determine the smallest (minimum) and largest (maximum) values directly. To find the quartiles, split the data into two halves at the median, and then find the medians of these halves to determine the first and third quartiles.

For the given set {2,3,7,1,4,5,6,10,9,4,6,7}:

1. Arrange in order: 1, 2, 3, 4, 4, 5, 6, 6, 7, 7, 9, 10
2. Minimum value (first term): 1
3. First quartile (median of the lower half): 4
4. Median (second quartile): (5+6)/2 = 5.5
5. Third quartile (median of the upper half): 7
6. Maximum value (last term): 10
7. Width of IQR: Third quartile - First quartile = 7 - 4 = 3

To visually represent this data, a box plot can be constructed. It will reflect the five number summary with a box stretching from the first to the third quartile and 'whiskers' extending to the minimum and maximum values.