Almost every quantitative results chapter opens with descriptive statistics, and almost every one of them is expected to report a measure of central tendency alongside a measure of spread. Reporting a mean with nothing beside it tells an examiner very little.
Paste your numbers — semester marks, questionnaire responses, field measurements — and this calculator returns the full set at once, with sample and population standard deviation shown separately.
The mean uses every value, so a single extreme observation drags it. The median is the middle value once sorted and barely moves in response to outliers, which is why income and land holding are almost always reported as medians in Nepali survey work.
Report both when your data is skewed, and the gap between them tells the reader how skewed it is. Where a handful of large values pull the mean well above the median, presenting the mean alone misrepresents the typical case — and an examiner who knows the dataset will notice.
The mode is the most frequent value and the only one of the three that works for categorical data — the most common district, caste group or response option. For continuous measurements it is often meaningless, because no two values repeat exactly.
Where nothing repeats, this tool reports no mode rather than listing every value. Where several values tie, all of them are modes and the distribution is bimodal — worth investigating rather than glossing over, since two clear peaks usually means two distinct groups have been combined in one dataset.
Divide by n−1 when your numbers are a sample from a larger population you want to draw conclusions about. Divide by n only when you have measured every member of the group you are describing. Almost all student research is the first case, so the sample figure is what belongs in your results chapter.
The n−1 correction exists because a sample's spread systematically understates the population's. The difference is negligible in large samples and pronounced in small ones — which is exactly the situation in most Master's fieldwork, so choosing correctly matters more here than it would elsewhere.
Convention is to report the mean with the standard deviation in brackets, to a consistent number of decimal places — usually two. State n for each variable, particularly where missing responses mean it differs between items.
Put the figures in a table and use the text to interpret them rather than to read them aloud. A results section that narrates every number in a table it has just presented is the commonest padding in a thesis, and it displaces the analysis an examiner is actually looking for.
The mean for roughly symmetric data, and both when the data is skewed — the gap between them shows the reader how skewed it is.
Sample (n−1) in almost all student research, because your data is a sample from a larger population. Population (n) applies only if you measured everyone.
Then there is no mode. That is a genuine result, and it does not mean every value counts as a mode.
Mean with standard deviation in brackets, to two decimal places, with n stated. Put them in a table and use the text to interpret rather than restate.
Yes. Commas, spaces, tabs and line breaks all work, and non-numeric entries are ignored and counted for you.