Performance indicators often see 80 quartile, 90 quartile these indicators, what are they, is how to calculate, this article to help you to solve the puzzle. The 80th percentile is a percentage. It should be called the 80th percentile. It can be understood that 80% of the numbers in the descending order are less than 80 fractions as shown in the figure below

What’s a percentile

In statistical terms, if a set of data is sorted from smallest to largest and the corresponding cumulative percentile is calculated, the value of the data corresponding to a certain percentile is called the percentile of that percentile. Can be expressed as: A group of N observed values are arranged in numerical size. For example, the value at the p% position is called the p-percentile.

Percentage calculation method:

Method 1:

The following steps show how to calculate the PTH percentile.

  • Step 1: Sort the raw data in ascending order (that is, from smallest to largest).
  • Step 2: Calculate the index I = NP %
  • Step 3:
    • If I is not an integer, round I up. The adjacent integer greater than I is the position in the PTH percentile.
    • If I is an integer, the p-th percentile is the average of the i-th term and the (I + L) term data.
For example, if the sequence S is > 3, 2, 5, > 4, 6, 7, the first step is sorted, 2, 3, 4, 5, 6, 7, the second step I =6 *0.8 =4.2, the third step I =4.2 is not an integer, rounded up by 5, then S> =6 is the 80-quantile of the sequenceCopy the code
2, 3, 4, 5, 6 step 2 I = 5*0.8 =4 step 3 I =4 is an integer, (L> + L>) / 2, that is, (5 + 6) / 2 = 5.5 is the 80th quantile of this sequenceCopy the code

Method 2:

In addition to the above methods, I will introduce another method, which is used by SPSS, one of the methods used by SAS, and also used by Excel’s PERCENTILE.EXC function.

  • Step 1: Arrange n variable values from small to large, and X(j) represents the JTH number in the sequence.
  • Step 2: Calculate the exponent, set (n+1)P%=j+g, j is the integer part, g is the decimal part.
  • Step 3:
    • When g=0: P percentile =X(j);
    • P percentile =g*X(j+1)+(1-g) when G ≠0X(j)=X(j)+g[X (j + 1) – (j) X].
For example, find the number X: 2, 4, 3, 5 of the 80 fractions of the first step sorted, 2, 3, 4, 5 of the second step I = (4+1)*0.8 = 4, the integer part j is 4, the decimal part g is 0 g=0, then the 80 quantile =X(j)=X(4) = 5Copy the code
For example, find the sequence X: > 3, 2, 5, > 4, 6, 7 80 quantile in the first step, 2, 3, 4, 5, 6, 7 2 step I = (6+1) * 0.8 = 5 + 0.6 integer part j is 5, the decimal part g is 0.6, the third step g=0.6 is not 0, So 80 quantile = 0.6 * (5 + 1) + X (1-0.6) * X (5) = 0.6 * 7 + 0.4 * 6 = 4.2 + 2.4 = 6.6 (5) = X + 0.6 * [X (6) - (5)] X = 6 + 0.6 * 7 [6] = 6.6Copy the code