Summarise three to fifty values with ordered data, mean, median, range and population standard deviation plus interpretation guidance.
Choose an example or type the known values, then calculate to see the answer and working.
A data summary should describe both centre and spread. This calculator orders an ungrouped list, then reports mean, median, range and population standard deviation. Each measure sees the data differently. The ordered values remain visible in the working so a reader can identify impossible entries, repeated observations and outliers before interpreting the summary.
Use it for three to fifty observations that represent the same variable and unit. The standard deviation treats the entered list as the complete population. If the values are a sample used to estimate a wider population, a sample-standard-deviation formula uses a different denominator. Grouped data, weighted frequencies and missing values need a more explicit model.
Mean or median locates a typical position, while range and standard deviation describe variation. Two groups can share a mean but differ greatly in consistency.
Each value's deviation from the mean is squared, averaged and square-rooted. Squaring prevents positive and negative deviations from cancelling and gives larger departures more influence.
A smaller spread can mean greater consistency, but consistency is not automatically better. Similar test scores and similar waiting times may have different practical meanings and targets.
| Mistake | Why it fails | Better check |
|---|---|---|
| Entering category labels as numbers | Codes such as class 1, 2 and 3 may not have meaningful numerical distances. | Summarise quantitative observations only with these measures. |
| Removing a repeated value | Duplicates often represent real separate observations and affect every measure. | Keep one entry for each observation unless data cleaning justifies removal. |
| Calling population SD a sample estimate | The denominators N and N - 1 answer different statistical purposes. | State that this tool reports population standard deviation for the entered list. |
An extreme value or skewed distribution can pull the mean while leaving the middle position relatively stable.
Yes. Commas and semicolons are accepted as separators, with a maximum of fifty finite values.
Not automatically. It means greater spread in the original unit; the practical judgement depends on what was measured.
The six observations are already in order and use one common unit.
Estimate the sign, scale, range or likely form of the answer before calculating. A prediction makes an input error easier to notice.
Add the values to obtain 110, then divide by 6 for a mean of about 18.33.
Average the two middle values, 18 and 18, so the median is 18.
Subtract the extremes for a range of 25 - 12 = 13.
Square each distance from 18.33, average those six squares and take the root for the population standard deviation.
The result points to related practice, but the best next step depends on what the learner could explain without help.