rank the following in increasing order and find the position and value of the 11th percentile show all work. 7 5 3 2 9 6 4 3 8 5 5 8

To rank the given numbers in increasing order, we can start by arranging them from smallest to largest:

2, 3, 3, 4, 5, 5, 5, 6, 7, 8, 8, 9

Now, to find the position and value of the 11th percentile, we need to perform the following steps:

Step 1: Calculate the rank position corresponding to the 11th percentile.
- The rank position is given by the formula: (percentile/100) * (n+1), where n is the total number of data points.
- In this case, n = 12 (since there are 12 data points).
- So, the rank position for the 11th percentile is (11/100) * (12 + 1) = 1.21 (rounded to two decimal places).

Step 2: Determine the value at the rank position.
- Since the rank position is not a whole number, we need to interpolate to find the value.
- The integer part of the rank position (1) corresponds to the 1st smallest value.
- The decimal part of the rank position (0.21) is used for interpolation.
- Interpolation involves determining the value between two consecutive data points.
- In this case, the value lies between the 1st and 2nd data points: 2 and 3.

Step 3: Perform interpolation to find the value.
- Interpolation is done using the formula: lower value + (decimal part x difference between the two values)
- In this case, the lower value is 2, and the higher value is 3.
- The difference between the two values is 3 - 2 = 1.
- So, the interpolated value is 2 + (0.21 x 1) = 2 + 0.21 = 2.21.

Therefore, the value at the 11th percentile is 2.21, and it is found at the rank position of 1.21.