rank the following data in increasing order and find the position and value of the 94,51st percentile. show all work.

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

To rank the given data in increasing order, follow these steps:

Step 1: Arrange the data in ascending order:
0, 0, 1, 4, 4, 4, 5, 7, 8, 9, 9, 9

Step 2: Calculate the percentile rank:
To find the position and value of the 94.51st percentile, we first need to calculate the percentile rank.

Percentile rank (PR) is calculated using the following formula:

PR = (P/100) × (N + 1)

Where P is the percentile value (94.51 in this case), and N is the total number of data points (12 in this case).

Substituting the values into the formula, we have:

PR = (94.51/100) × (12 + 1)
PR = 0.9451 × 13
PR ≈ 12.286

Step 3: Determine the position:
Since percentile rank represents a position, we round up the percentile rank to the nearest whole number to determine the position.

Rounding up 12.286 to the nearest whole number gives us 13.

Step 4: Find the value:
To find the value at the 94.51st percentile, we locate the 13th data point in the sorted list.

The 13th value is 9.

Therefore, the position of the 94.51st percentile is 13, and the corresponding value is 9.