Academics · Study Skills · Math

Three kinds of
middle, with all
the working.

Paste a list of numbers. The calculator finds the mean, median, mode and range, writes out each step the way a teacher would want it shown, and draws a dot plot so you can see why the three answers differ.

Find the centerWhat you get

The calculator

The worked example is made up: how many minutes 12 students spent on homework one night. Nothing you type leaves this browser.

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What you get

Academics · Study SkillsFree

What you finish with
The mean, median, mode and range of your numbers, each step written out, the numbers in order, a frequency table and a dot plot, and a note on which center fits your data. It prints as a one-page summary and downloads as a spreadsheet.
Who it is for
Middle school students checking their work, families helping with homework, and math teachers and tutors who want a worked example to show.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Up to 500 numbers. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The Study Skills space in Caveat Academics.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Say what the numbers are, so the printout makes sense later.
  2. Type or paste the numbers.
  3. Read the mean, median, mode and range, then the steps under them.
  4. Look at the dot plot to see whether a few far-off values pull the mean away.
  5. Print the summary or download the spreadsheet.

Find the center

How each center is found

Add and share, put in order, count.

The 12 values in order2025303030354045456090120median: halfway between 35 and 40 = 37.5mode: 30 appears 3 times (light blue)mean: 570 ÷ 12 = 47.5, pulled up by 90 and 120The 12 values in order2025303030354045456090120median: halfway between 35 and 40 = 37.5mode: 30 appears 3 times (light blue)mean: 570 ÷ 12 = 47.5, pulled up by 90 and 120
In the worked example the two middle values, 35 and 40, give the median; 30 is the mode; the two long homework nights pull the mean above both.

The three centers

The mean adds every value and divides by how many there are: what each would get if the total were shared equally. The median puts the values in order and takes the middle one, or the number halfway between the two middle ones when the count is even. The mode is the value that appears most often; a list can have more than one mode, or none when nothing repeats. The range is the largest value minus the smallest.

Which one to use

When a few values sit far from the rest, as with two very long homework nights, the mean moves toward them and the median does not. That is why reports of incomes and house prices use the median. The mode is the only center that works for categories, such as favorite sports.

Sources

  1. Common Core State Standards for Mathematics, Grade 6, Statistics and Probability (6.SP.A.3, 6.SP.B.5): measures of center and variation and choosing among them.
  2. National Council of Teachers of Mathematics. Principles and Standards for School Mathematics, Data Analysis and Probability standard.
  3. U.S. Census Bureau, Statistics in Schools (census.gov/schools): activities on mean and median with real data.
  4. NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.1, Measures of Location (itl.nist.gov).

The worked example is made up. Your numbers stay in this browser. Support: team@caveatacademic.com.