For statistics tutors

How to teach statistics online on a whiteboard: z-scores on a normal curve, step by step

Intro statistics is full of pictures: a curve, a shaded area, a number line. Online, the question is where you draw them and whether your student draws them with you. This page walks through one lesson, z-scores on a normal curve, and says plainly what Instaboard does for statistics: curves are freehand ink, and there is no statistical software, no normal table, no calculator and no data import.

Updated November 2, 2026

An Instaboard statistics lesson board: two hand-drawn normal curves for quiz scores with mean 70 and standard deviation 8, a z-score of 2 worked for a score of 86 with the upper tail shaded, the student's turn for a score of 62 in blue with the lower tail shaded, working back from z to a score, homework and common mistakes to redo — A ready z-score lesson: the normal curve drawn by hand, the worked example in ink, your student's turn in blue, homework and common mistakes. Open it and it's yours. Swipe to see the whole board.

The short answer

Use the board as a curve-and-working page. Draw the normal curve, mark the mean and the scores, work the z-score beside it, then let your student do the next score on the same page.
The curve is freehand ink on Instaboard. It is not to scale, and there is no statistical software, no normal table, no calculator and no data import. For exact probabilities, use a calculator or software and keep the board for the reasoning.
Work from the methods and materials the student's class uses. In a 2025 r/TutorsHelpingTutors thread on tutoring AP Statistics, one reply says students want the same methods and style of problems their teachers use, and recommends real AP and IB materials for practice.
Students can view with no account but need a free sign-in to write. Free calls run 60 minutes per call, with a warning 10 minutes before the end; Pro ($5 a month billed yearly) has no limit.

What a lesson on the board looks like

The call sits on top of the board, so you talk and write in the same place. You draw the curve and work the first score, your student works the next one in their own colour, and you tick it.

You draw and calculate, your student does the next one in blue, you tick it. One link for the call and the board.

What a statistics tutor does on a whiteboard

In the 2025 r/TutorsHelpingTutors thread, a new AP Statistics tutor describes spending two to four hours preparing each lesson and then teaching it for the first 20 to 40 minutes, and asks what to charge; one experienced reply says students show up with their assignments and want to re-work their teacher's examples with the numbers changed, and suggests asking to see their notes and corrected quizzes. That is one tutor's view, and the thread is about rates as much as method. It does point to four jobs for a board:

Draw the picture. A curve with the mean marked and the score you are asking about.
Work the calculation beside it, one line at a time, so the student sees the order.
Change the numbers and let the student do the next case in their own colour.
Go both ways. From a score to a z-score, and back from a z-score to a score.

A tablet or pen tablet makes curves and numbers faster than a mouse; see which pen tablet to buy and online tutoring setup. For the maths habits behind it, see how to teach math online and an online whiteboard for math.

A z-score lesson in five steps

OpenStax Introductory Statistics 2e, section 6.1, defines the z-score as how many standard deviations a value x is above (positive) or below (negative) the mean, calculated as z = (x - mean) / standard deviation, and shows the way back as x = mean + z times the standard deviation. The same section states the Empirical Rule: about 68% of values lie within one standard deviation of the mean and about 95% within two. The board follows that order with our own made-up numbers for quiz scores with a mean of 70 and a standard deviation of 8:

Ask first: a quiz score of 86, is that high? Let the student say what else they would need to know before you write anything.
Draw the curve and mark the mean, 70, and the scores one and two standard deviations either side: 54, 62, 78 and 86.
Work z for 86: (86 - 70) / 8 = 2, so 86 is two standard deviations above the mean. About 95% lie within two, so about 5% lie outside, and by symmetry about 2.5% score above 86.
Student's turn, 62: (62 - 70) / 8 = -1, one standard deviation below the mean. About 68% lie within one, so about 32% lie outside and about 16% score below 62.
Go backwards: a z-score of 1.5 means x = 70 + 1.5 x 8 = 82.

Score x	z-score	Where it sits	Share of scores (about)
86	(86 - 70) / 8 = 2	2 SDs above the mean	About 2.5% score above 86
62	(62 - 70) / 8 = -1	1 SD below the mean	About 16% score below 62
82	z = 1.5, so x = 70 + 1.5 x 8	1.5 SDs above the mean	Not worked on the board

Swipe the table sideways to see every column.

The z-score formula, its sign rule and the Empirical Rule follow OpenStax Introductory Statistics 2e, section 6.1 (read November 2, 2026). The split of the outside share into two equal tails is our step, from the curve's symmetry, and 68% and 95% are the Empirical Rule's approximate figures. The quiz scores are invented for this lesson, not measured data.

The point worth saying out loud is the red note on the board: a score below the mean gives a negative z. The usual slips are forgetting to subtract the mean first, dropping the sign, and treating 68 and 95 as exact. OpenStax section 6.2 shows how to get exact areas for values that are not whole standard deviations from the mean: with a normal table or a calculator or computer, not by hand.

Drawing statistics on Instaboard

On Instaboard you draw with the pen, like a whiteboard in a room. Here is what that means, so you can decide before the lesson:

A freehand curve. The bell, the axis, the mean line and the shading are pen strokes, as on the board above. They are not to scale and the board does not check them.
Hand-written working. Fractions, z-scores and answers are written, not typed. Cards and lists hold typed notes if you want a tidy checklist beside the curve.
The worksheet or past-paper question. Import the student's PDF and write on it. Each imported PDF uses one of the 5 free boards.
A small table of data. You can write one by hand or use a list of cards, but the board does not calculate anything from it.

No statistical software, no normal table, no calculator

Instaboard has no statistical software, no built-in normal table or probability calculator, no data import and no plots from data. Equation cards typeset a formula, and a Desmos graph can sit on the board as a snapshot that opens the full calculator, but it needs a connection. Exact probabilities need a calculator, a table or software; use those and keep the board for the reasoning.

When another tool is the better choice

Your student needs to run software on data. A 2026 open-access paper from the University of Melbourne on small-group university statistics classes (Fijn and Duffy, International Journal of Mathematical Education in Science and Technology) says touchscreen electronic whiteboards have progressed to where students working together can reach the full suite of statistical software. Instaboard does not run statistical software, so it cannot do that.
You need exact probabilities. Use the calculator, table or software your student's course uses.
Your student only needs to watch. Screen-share annotation on your own platform is enough if you do not need them to write.
Your platform already has a whiteboard you like. Keep it if it works for you.
You want a recording of the lesson. Instaboard does not record.

The Melbourne abstract says the evaluation found no significant differences in any of the measured areas, and notes that it compares a redesigned course using an emerging technology with well-established traditional practice. It is about university small-group classes, not private tutoring, so it is not evidence that a whiteboard improves results. Instaboard fits when you teach by drawing, you want the student to do the next calculation, and you want the call, the curve and the working on one link.

Use the lesson board in five steps

Open the statistics board above and make it yours.
Send your student the link, or press Call on the board so the lesson runs in one place. They sign in free once to write.
Swap in your topic. Change the mean and the standard deviation to the ones in your student's problem, or redraw the curve for another idea.
Let the student do the next case in their own colour and say what the answer means in words.
Leave the board open as the revision sheet and start the next lesson from it.

The same pattern works for other subjects: how to teach math online, how to teach economics online and how to teach accounting online. To keep notes across lessons, see the tutoring session notes template.

What Instaboard doesn't do for statistics

No statistical software, no normal table, no calculator. Curves, areas and working are hand-drawn ink, and freehand curves are not to scale.
No data import and no plots from data. The board does not calculate or chart anything.
No handwriting reading. Handwritten numbers are not searchable or checked.
Whole-stroke eraser only. You cannot rub out part of a line; erase the stroke and redraw it.
No recording of the lesson, no class mode, no scheduling.
Students sign in to write. Anyone with the link can view; writing needs a free sign-in. Free calls run 60 minutes per call, with a warning 10 minutes before the end.
Free covers 5 boards. Each imported PDF uses one of them. Pen strokes do not count toward the 150-item limit; cards and lists do.
Free boards are shared by link, so use first names only.

Start from the ready board

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Questions

How do I teach statistics on an online whiteboard?

Draw the curve, mark the mean and the score, work the z-score beside it line by line, then let the student do the next score on the same board. Import the student's worksheet as a PDF so you both write on the real question.

Can I use Instaboard for statistics software or exact probabilities?

No. Instaboard has no statistical software, normal table or calculator, and it cannot import data. Use it to teach the reasoning by drawing and writing, and use a calculator, table or software for exact numbers.

What is a z-score?

It tells you how many standard deviations a value is above or below the mean: z = (x - mean) / standard deviation. Values above the mean have positive z-scores and values below have negative ones, according to OpenStax Introductory Statistics 2e, section 6.1.

What is the 68-95-99.7 rule?

The Empirical Rule says that for a normal distribution about 68% of values lie within one standard deviation of the mean, about 95% within two and about 99.7% within three (OpenStax Introductory Statistics 2e, section 6.1). The figures are approximate.

Do I need a tablet to teach statistics online?

No, but curves and numbers are slow with a mouse. A touchscreen laptop, an iPad or a pen tablet helps.

Is Instaboard free?

Yes. The free plan includes 5 boards, 150 cards and items across your account (pen strokes, arrows and sections don't count), 3 images and 1 file per board, unlimited collaborators and video calls up to an hour. Pro is $5 a month billed yearly ($59.99 a year), or $7.99 monthly, and the people you invite join free.