rank the following in increasing order and find the position and value of the 91st percentile show all work.

4,,5,4,9,9,1,0,7,4,8,0,9

To rank the given set of numbers in increasing order, you need to arrange them from the smallest to the largest:

0, 0, 1, 4, 4, 4, 5, 7, 8, 9, 9, 9

Now, to find the position and value of the 91st percentile, you first need to calculate its position using the following formula:

Position = (P / 100) * (N + 1)

Where P is the desired percentile (91 in this case), and N is the number of data points (12 in this case).

Calculating the position:

Position = (91 / 100) * (12 + 1) = 10.92

Since you cannot have a fractional rank, you need to round up to the next whole number. Therefore, the position is 11.

To find the value at the 91st percentile, you can look at the element in the 11th position within the sorted data set:

Value at 91st percentile = 9

So, the position of the 91st percentile is 11, and its value is 9.