This tool takes a list of numbers and gives you the centre and spread, with each step shown. It helps students who want to check a calculation, see how an extreme value changes the answer, or confirm which formula they should be using.
Free tool · Mathematics
Descriptive statistics explorer
You know the formulas but lose marks dividing by n when you should divide by n minus one.
Everything you enter stays on this device.
How do I use it?
- Type your numbers, separated by commas, spaces or new lines. Use value:frequency for repeats.
- Choose population (divide by n) or sample (divide by n − 1).
- Optionally type one extra value to see how an outlier changes each measure.
- Press “Calculate” and read the table, the dot plot and the working.
How does it work?
The tool sorts the data and finds the mean as the sum divided by n. The median is the middle value, or the average of the two middle values. The mode is the most frequent value, and “no mode” appears when every value occurs once.
Quartiles come from the medians of the lower and upper halves, with the median left out when n is odd. The variance is the sum of (x − mean)² divided by n or by n − 1, and the standard deviation is its square root.
When all your numbers are integers, the variance is also shown as an exact fraction. Empty input is rejected, and a one-item sample variance is marked unavailable.
A short worked example
Enter 1, 2, 3 with the population convention.
The mean is 2. The deviations are −1, 0 and 1, so the squares add to 2. Dividing by n = 3 gives a variance of 2/3, about 0.6667, and a standard deviation of about 0.8165.
Now change the convention to sample. The same sum of 2 is divided by 2, so the variance becomes 1. Only the divisor changed, which is why naming the convention matters.
What are its limits?
The tool works on a finite list of up to 500 values. It does not group data into class intervals or estimate from a histogram, so grouped questions with class boundaries still need your own midpoints. It cannot say which convention your exam question intends.
Where does it connect to the lessons?
Use it with dispersion of ungrouped data and its practice page. For tables with class intervals, continue to dispersion of grouped data.
If choosing formulas is the stumbling block, SPM Mathematics tuition gives you a teacher to practise with. The one-hour trial class (from RM50) is the first step.
Common questions
What is the difference between population and sample variance?
Population variance divides the sum of squared deviations by n. Sample variance divides by n − 1. The tool names the convention in the result, and your question or teacher decides which one to use.
Why is sample variance unavailable for one value?
It would need division by n − 1, which is 0 for a single value. Division by zero is undefined, so the tool says the value is unavailable.
Can I enter a frequency table?
Yes. Write each value as value:frequency, for example 12:3 for three twelves. The tool expands the table into a list and calculates from it.
Why do my quartiles differ from my textbook?
Quartile methods for short lists differ between textbooks. The tool states the one it uses in the result, so check it against the method in your class.
A teacher can go through your own mistakes one by one in a one-to-one lesson, for example the choice of formula, and practise each until you can choose it without help.
- Online one-to-one lessons for your child with an experienced teacher.
- Your first class is a one-hour trial, from RM50. The fee is agreed before you book.
- Happy with the teacher? Continue with lessons of about 1.5 hours. If not, ask for another teacher.