What is the difference between sample and population standard deviation?

Dividing by the count, or by the count minus one. Population is right when your numbers are the entire set. Sample is right when they are a sample of something larger, which they usually are. On a small set the two differ noticeably, so the tool names which one it used rather than leaving you to guess.

Why does it sometimes say there is no mode?

Because a set where every value appears once genuinely has no mode. Returning the first value would be a wrong answer dressed as an answer. If two values tie for most common, both are listed, since a set can have two modes.

How should I separate the numbers?

However they already are. Commas, spaces, tabs, semicolons and new lines all work, so a column pasted from a spreadsheet needs no cleaning up first.

Mean, Median and Mode Calculator

Every average at once, and both deviations named.

Numbers

Standard deviation

SamplePopulation

Every average at once, and both deviations named.

How to use it

Paste the numbers. Separated by commas, spaces, tabs or new lines. All of them work.
Choose the deviation. Sample if these are part of something larger, which is the usual case.
Read the table. Count, sum, mean, median, mode, range and deviation together.

When you would use this

Mean, median and mode answer different questions about the same numbers, and the reason to show all of them together is that the difference between them is usually the interesting part. A mean far above the median means a few large values are pulling it. Two things here are more careful than they look. The mode is every value that appears most often, not the first one found. A set can genuinely be bimodal, and reporting one of two modes is a wrong answer rather than a simplification. A set where everything appears once has no mode, and it says so. Standard deviation comes in two forms that differ only in whether you divide by the count or by the count minus one, and on a small set they differ enough to matter. Sample is the default because most data is a sample of something larger, and the label always says which was used. Numbers are read however they were pasted: commas, spaces, tabs, semicolons or new lines, so a column from a spreadsheet works without being tidied first.

Questions

What is the difference between sample and population standard deviation?: Dividing by the count, or by the count minus one. Population is right when your numbers are the entire set. Sample is right when they are a sample of something larger, which they usually are. On a small set the two differ noticeably, so the tool names which one it used rather than leaving you to guess.
Why does it sometimes say there is no mode?: Because a set where every value appears once genuinely has no mode. Returning the first value would be a wrong answer dressed as an answer. If two values tie for most common, both are listed, since a set can have two modes.
How should I separate the numbers?: However they already are. Commas, spaces, tabs, semicolons and new lines all work, so a column pasted from a spreadsheet needs no cleaning up first.