Python Pandas - 如何通过描述函数计算 25 个百分位
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Python Pandas - how is 25 percentile calculated by describe function
提问by Gublooo
For a given dataset in a data frame, when I apply the describefunction, I get the basic stats which include min, max, 25%, 50% etc.
对于数据框中的给定数据集，当我应用该describe函数时，我会得到基本统计数据，包括最小值、最大值、25%、50% 等。
For example:
例如：
data_1 = pd.DataFrame({'One':[4,6,8,10]},columns=['One'])
data_1.describe()
The output is:
输出是：
One
count 4.000000
mean 7.000000
std 2.581989
min 4.000000
25% 5.500000
50% 7.000000
75% 8.500000
max 10.000000
My question is: What is the mathematical formula to calculate the 25%?
我的问题是：计算 25% 的数学公式是什么？
1) Based on what I know, it is:
1）据我所知，它是：
formula = percentile * n (n is number of values)
In this case:
在这种情况下：
25/100 * 4 = 1
So the first position is number 4 but according to the describe function it is 5.5.
所以第一个位置是数字 4 但根据描述函数它是5.5。
2) Another example says - if you get a whole number then take the average of 4 and 6 - which would be 5 - still does not match 5.5given by describe.
2）另一个例子说 - 如果你得到一个整数，那么取 4 和 6 的平均值 - 这将是 5 - 仍然与5.5描述给出的不匹配。
3) Another tutorial says - you take the difference between the 2 numbers - multiply by 25% and add to the lower number:
3）另一个教程说 - 你取两个数字之间的差 - 乘以 25% 并添加到较低的数字：
25/100 * (6-4) = 1/4*2 = 0.5
Adding that to the lower number: 4 + 0.5 = 4.5
将其添加到较低的数字中： 4 + 0.5 = 4.5
Still not getting 5.5.
还是没有得到5.5。
Can someone please clarify?
有人可以澄清一下吗？
采纳答案by Nikolas Rieble
In the pandas documentationthere is information about the computation of quantiles, where a reference to numpy.percentile is made:
在Pandas文档中有关于分位数计算的信息，其中对 numpy.percentile 进行了引用：
Return value at the given quantile, a la numpy.percentile.
返回给定分位数的值，一个 numpy.percentile。
Then, checking numpy.percentile explanation, we can see that the interpolation method is set to linearby default:
然后，检查 numpy.percentile解释，我们可以看到插值方法默认设置为线性：
linear: i + (j - i) * fraction, where fraction is the fractional part of the index surrounded by i and j
线性：i + (j - i) * 分数，其中分数是被 i 和 j 包围的索引的小数部分
For your specfic case, the 25th quantile results from:
对于您的特定情况，第 25 个分位数来自：
res_25 = 4 + (6-4)*(3/4) = 5.5
For the 75th quantile we then get:
对于第 75 个分位数，我们得到：
res_75 = 8 + (10-8)*(1/4) = 8.5
If you set the interpolation method to "midpoint", then you will get the results that you thought of.
如果你将插值方法设置为“中点”，那么你就会得到你想到的结果。
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回答by orli Zhu
I think it's easier to understand by seeing this calculation as min+(max-min)*percentile. It has the same result as this function described in NumPy:
我认为通过将此计算视为min+(max-min)*percentile更容易理解。它具有与 NumPy 中描述的此函数相同的结果：
linear: i + (j - i) * fraction, where fraction is the fractional part of the index surrounded by i and j
线性：i + (j - i) * 分数，其中分数是被 i 和 j 包围的索引的小数部分
res_25 = 4+(10-4)*percentile = 4+(10-4)*25% = 5.5
res_75 = 4+(10-4)*percentile = 4+(10-4)*75% = 8.5
