A confidence interval for the mean from your sample: x̄ ± t(0.975, n−1) · s/√n. Paste the numbers, get the interval plus the standard error and margin of error.
The critical value comes from the exact t distribution (incomplete beta), so small samples get correctly wider intervals — at n = 5 the multiplier is 2.78, not the 1.96 many people quote from memory. A proportion mode uses the Wilson score interval, which stays sane near 0 and 1 where the textbook Wald interval misbehaves.
Frequently asked questions
What does "95%" mean here?
It describes the procedure: across many random samples, 95% of the intervals constructed this way cover the true mean. The true value is not random — the interval is.
Why is my interval so wide?
Width is driven by the sample standard deviation and, through the square root, by n. Halving the width needs four times the data — see the article on inferential statistics for the arithmetic.
中文说明
用你的样本算均值的置信区间：x̄ ± t(0.975, n−1) · s/√n。粘贴数据，得到区间以及标准误与误差边际。
临界值来自精确 t 分布（不完全 beta 函数），小样本自动得到更宽的区间——n = 5 时乘数是 2.78 而不是很多人背的 1.96。比例模式用 Wilson 得分区间，在接近 0 和 1 的地方不像教科书 Wald 区间那样失真。
常见问题
这里的 95% 是什么意思？
它描述的是构造程序：多次随机抽样下，这样构造的区间有 95% 会盖住真值。真值不随机——随机的是区间。
为什么我的区间这么宽？
宽度由样本标准差和（经平方根）样本量决定。宽度减半需要四倍数据——算术细节见推断统计一文。