First, we need to be clear about the percentage to be calculated. For example, if you want to calculate the 70% percentile, you need to find the value at the 70% position in the dataset.
Here are the steps to calculate the percentage:
Step 1: Arrange the data sets from small to large.
Step 2: Determine where to calculate the percentage. If you want to calculate the percentile of P%, you can use the following formula:
R = (P/ 100) * (N + 1)
Where r represents the decimal point where P% is located, and n represents the size of the data set (that is, the number of data).
Step 3: Calculate the integer and decimal parts of R, where the integer part indicates the subscript of the target position and the decimal part indicates the relative position at the target position.
Step 4: According to the integer part of R, determine the data point corresponding to the percentile. If the fractional part of r is not 0, interpolation calculation is needed. That is, the numerical value of the target position is calculated by interpolation based on the values corresponding to the two positions determined by the integer part.
For example:
Suppose there are the following data sets: 10, 12, 15, 18, 22, 28. We need to calculate the percentage of 80%.
Step 1: Sort the data sets in descending order: 10, 12, 15, 18, 22, 28.
Step 2: Calculate the position r: r = (80/100) * (6+1) = 5.6.
Step 3: The integer part of R is 5 and the decimal part is 0.6.
Step 4: Determine the values corresponding to the two positions according to the integer part. In this example, the integer part is 5, and the corresponding two positions are the fifth value 18 and the sixth value 22. Because the fractional part is 0.6, the numerical value of the target position can be calculated by linear interpolation. The formula for interpolation calculation is:
Value = (1-fraction) * value 1+fraction * value 2
Where Value represents the numerical value of the target position, Value 1 and Value2 respectively represent the numerical values corresponding to the two positions determined by the integer part, and Fraction represents the fractional part.
According to this formula, we get:
Value = (1-0.6) *18+0.6 * 22 = 20.4.
Therefore, the 80% percentile is 20.4.
These are the basic steps to calculate the percentile. Please note that in practical application, other methods may be used to calculate percentile, such as linear interpolation method and weighted average method. Choose the appropriate method according to the specific situation.