Rank the following data in increasing order and find the position and value of the 56th percentile. Please show all of your work.
0 1 6 8 9 9 8 6 3 1 0 9
Show your work and I will be glad to check it.
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How do I find the position and value of the 56th percentile?
With 12 digits, the 50th percentile (median) will be between the two 6s. Each number is .08 of the distribution, so you cannot find the 56th percentile exactly, but it would be between the second 6 and the 8.
To rank the data in increasing order, we need to sort the data from lowest to highest. Let's write down the given data in increasing order:
0 0 1 1 3 6 6 8 8 9 9 9
Now, to find the position and value of the 56th percentile, we need to follow these steps:
Step 1: Calculate the percentile rank position.
- First, calculate the total number of data points: in this case, it is 12.
- Next, calculate the percentile rank position by using the formula: (percentile/100) * (total data points + 1). In this case, the percentile is 56.
- Calculate: (56/100) * (12 + 1) = 0.56 * 13 = 7.28
Note: Since the percentile rank position is not a whole number, we need to round it up to the nearest whole number, which is 8.
Step 2: Find the value at the rounded percentile rank position.
To find the value at the 8th position, we look at the sorted data:
0 0 1 1 3 6 6 8 8 9 9 9
The value at the 8th position is 8.
Therefore, the position of the 56th percentile is 8, and the corresponding value is 8.