🔟 十分位数计算器（D1–D9，含位置与插值）Decile Calculator (D1–D9 with Positions)
粘贴一组数据，一次算出全部九个十分位数 D1–D9，可选两种常用定义：(n+1)p（Excel PERCENTILE.EXC、Minitab）或 (n−1)p+1（Excel PERCENTILE.INC、NumPy 默认），并列出每个十分位的位置和插值。本地处理。Paste a data set to get all nine deciles D1–D9 at once, using either of two common definitions: (n+1)p (Excel PERCENTILE.EXC, Minitab) or (n−1)p+1 (Excel PERCENTILE.INC, NumPy default), with the position and interpolation for each decile. Processed locally.
使用说明与常见问题How-to & FAQ
「十分位数计算器（D1–D9，含位置与插值）」是什么？What is the Decile Calculator (D1–D9 with Positions) tool?
粘贴一组数据，一次算出全部九个十分位数 D1–D9，可选两种常用定义：(n+1)p（Excel PERCENTILE.EXC、Minitab）或 (n−1)p+1（Excel PERCENTILE.INC、NumPy 默认），并列出每个十分位的位置和插值。本地处理。Paste a data set to get all nine deciles D1–D9 at once, using either of two common definitions: (n+1)p (Excel PERCENTILE.EXC, Minitab) or (n−1)p+1 (Excel PERCENTILE.INC, NumPy default), with the position and interpolation for each decile. Processed locally.
如何使用「十分位数计算器（D1–D9，含位置与插值）」？How do I use the Decile Calculator (D1–D9 with Positions) tool?
在「十分位数计算器（D1–D9，含位置与插值）」中，填写「数据（空格、逗号或换行分隔）」、「定义」等参数，结果会随输入实时计算并显示在下方。In the Decile Calculator (D1–D9 with Positions): Fill in "Data (spaces, commas or new lines)", "Definition"; results are recalculated instantly as you type.
十分位数是什么？What are deciles?
十分位数把排好序的数据分成十等份：D1 以下约有 10% 的数据，D5 就是中位数，D9 以下约有 90%。Deciles split sorted data into ten equal parts: about 10% of the values lie below D1, D5 is the median and about 90% lie below D9.
为什么不同软件结果不一样？Why do different programs give different answers?
十分位（百分位）有好几种定义。(n−1)p+1 是 Excel 的 PERCENTILE.INC 和 NumPy 的默认方法；(n+1)p 是 Excel 的 PERCENTILE.EXC、Minitab 和很多教科书的方法。数据越多，两者差别越小。There are several definitions. (n−1)p+1 is what Excel's PERCENTILE.INC and NumPy use by default; (n+1)p is Excel's PERCENTILE.EXC, Minitab and many textbooks. The more data you have, the smaller the difference.
位置是小数怎么办？What if the position is not a whole number?
在相邻两个数之间按比例插值。例如位置 5.5 就取第 5 个和第 6 个数的中点；位置 1.9 就是第 1 个数加上到第 2 个数距离的 0.9。Interpolate between the two neighbours. Position 5.5 is halfway between the 5th and 6th values; position 1.9 is the 1st value plus 0.9 of the gap to the 2nd.
能举个计算实例吗？Can you show a worked example?
例如在「十分位数计算器（D1–D9，含位置与插值）」中填 数据（空格、逗号或换行分隔） = 1 2 3 4 5 6 7 8 9 10，定义 = (n−1)p+1（Excel PERCENTILE.INC…，结果区显示：数据个数 n：10；最小值 / 最大值：1 / 10；ℹ 位置 = (n−1)×k/10+1；位置不是整数时在相邻两个数之间线性插值For example, entering Data (spaces, commas or new lines) = 1 2 3 4 5 6 7 8 9 10, Definition = (n−1)p+1 (Excel PERCENTILE… in the Decile Calculator (D1–D9 with Positions) gives: Count n: 10; Min / max: 1 / 10; ℹ position = (n−1)×k/10+1; a fractional position interpolates linearly between the two neighbouring values
有哪些选项可以调整？What options can I adjust?
「十分位数计算器（D1–D9，含位置与插值）」的设置：「数据（空格、逗号或换行分隔）」默认 12, 15, 18, 22, 25, 27…；「定义」可选 (n−1)p+1（Excel PERCENTILE.INC / NumPy）、(n+1)p（Excel PERCENTILE.EXC / Minitab）（默认 (n−1)p+1（Excel PERCENTILE.INC / NumPy））。每次生成结果都按当前设置处理。Settings in the Decile Calculator (D1–D9 with Positions) — "Data (spaces, commas or new lines)" default 12, 15, 18, 22, 25, 27…; "Definition": (n−1)p+1 (Excel PERCENTILE.INC / NumPy), (n+1)p (Excel PERCENTILE.EXC / Minitab) (default (n−1)p+1 (Excel PERCENTILE.INC / NumPy)). The result always uses the current settings.
计算精度如何？How precise are the results?
「十分位数计算器（D1–D9，含位置与插值）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Decile Calculator (D1–D9 with Positions) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「十分位数计算器（D1–D9，含位置与插值）」免费吗？需要注册吗？Is the Decile Calculator (D1–D9 with Positions) free? Do I need an account?
「十分位数计算器（D1–D9，含位置与插值）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Decile Calculator (D1–D9 with Positions) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.