Rank the following data in increasing order and find the position and value of the 65th percentile. Please show all of your work.
2 1 6 3 4 7 0 0 0 7 5 8
Do you need help arranging this data in increasing order?
To rank the data in increasing order, we need to arrange the numbers from smallest to largest. Here is the sorted list:
0 0 0 1 2 3 4 5 6 7 7 8
To find the position of the 65th percentile, we need to first calculate the rank. The rank is equal to (percentile / 100) * (n + 1), where n is the total number of data points.
In this case, the percentile is 65, and the total number of data points is 12. Let's plug these values into the formula:
Rank = (65 / 100) * (12 + 1) = 0.65 * 13 = 8.45 (rounded to the nearest whole number, which is 8)
So, the position of the 65th percentile is the 8th value in the sorted list, which is 5.
To find the value corresponding to the 65th percentile, we can simply look up the 8th value in the sorted list, which is 5.
Therefore, the position of the 65th percentile is 8 and the corresponding value is 5.