# Estimating in ranges

> Three-point estimates that keep the spread: the expected value and standard deviation of each task, how to add several tasks, and how to say a date with its confidence.

- Course: [Project Management Without the Bureaucracy: Run One Project from Brief to Closure](https://productovi.com/courses/project-management-without-bureaucracy.md)
- Module: Estimates and the budget
- Lesson 13/32, ~25 min
- Source: https://productovi.com/courses/project-management-without-bureaucracy/estimating-in-ranges

## Where we are

**Alex Tutor:** It's November. The brief is signed, the work is broken into deliverables, and the schedule runs to 1 February. This module turns the plan into numbers Leo and Hanna can trust: dates in ranges, one buffer and a budget by month.

**Leo:** Danylo, when is the diagnostic test ready? I need one date for the marketing plan.

**Danylo:** Fourteen working days. If nothing breaks.

**Alex Tutor:** "If nothing breaks" is the real information, and the single number hides it. Ask for three numbers per task instead: optimistic, most likely and pessimistic.

**Sofia:** Isn't that just a polite way to avoid committing?

**Alex Tutor:** The opposite. A narrow range says the work is well known; a wide one says something is still unknown and shows where. Here's what Danylo and Vira wrote down.

**Dataset (CSV):** [Diagnostic test: three-point estimates](https://productovi.com/datasets/project-management-without-bureaucracy/estimating-in-ranges/klasna-physics-test-estimates.csv)

The three tasks run one after another. Estimates in working days.

- `task`: Task
- `owner`: Who answers for it
- `optimistic_days`: Optimistic: if everything goes well
- `likely_days`: Most likely
- `pessimistic_days`: Pessimistic: if the usual things go wrong

> **Exercise:** Writing the 40 questions is estimated at 3, 5 and 13 days. What does this range tell you **first**?

## One task: the expected value and the spread

**Vira:** Thirteen is real. Each question needs a worked solution and a diagram, and the illustrator draws the diagrams. If the drawings come late, I wait.

**Alex Tutor:** Good: now the range has a cause. Two quick numbers per task summarize it. The expected value weights the most likely case four times. The standard deviation is a sixth of the distance between the extremes.

$$
E = \frac{O + 4M + P}{6} \qquad \sigma = \frac{P - O}{6}
$$

*O: optimistic, M: most likely, P: pessimistic. E is the expected value, σ the standard deviation.*

**Alex Tutor:** For the questions: (3 + 4 × 5 + 13) ÷ 6 = 6 days, and (13 − 3) ÷ 6 ≈ 1.67 days. Notice that 6 is more than 5: the bad side is longer than the good side, so the expected value moves toward it.

**Danylo:** That matches my experience. Things rarely go three days better than planned. They often go a week worse.

> **Exercise:** Danylo estimates the trial with 20 learners and the fixes at 2, 3 and 10 working days. What is the **expected value** of this task, in working days?

**Alex Tutor:** And how wide is that same task? Try its standard deviation.

> **Exercise:** The trial with 20 learners and the fixes is estimated at 2, 3 and 10 working days. What is its **standard deviation**, in working days (two decimals)?

## Several tasks: add the variances

**Sofia:** Then the whole test is 6 + 6 + 4 = 16 days. And the spread is 1.67 + 0.67 + 1.33, about 3.67 days?

**Alex Tutor:** The first part is right: expected values add up. The second isn't. To combine spreads, square each standard deviation to get its variance, add the variances, then take the square root.

**Alex Tutor:** Here: 2.78 + 0.44 + 1.78 = 5.0, and the square root of 5 is about 2.24 days. Adding the standard deviations pretends every task hits its worst day at the same time.

**Danylo:** So three tasks together are more predictable than each one alone?

**Alex Tutor:** Relative to their size, yes: a bad week on one task is often offset by a good one elsewhere. That only holds if the tasks are independent. If one cause, like the illustrator, can delay all three, treat it as one risk.

> **Exercise:** The diagnostic test is three independent tasks in a row (questions, build, trial with fixes), with standard deviations of 1.67, 0.67 and 1.33 days. What is the standard deviation of the whole test?

**Alex Tutor:** One condition hides in that rule. True or false?

> **Exercise:** **True or false:** if the outside illustrator can delay all three test tasks at once, you may still add their variances as if the tasks were independent.

## A range says how sure you are

**Alex Tutor:** Now say it as a range. Two standard deviations either side: 16 ± 4.5, so about 11.5 to 20.5 working days. Under the usual bell-shaped assumption, that range holds about 19 times in 20.

**Leo:** I still have to put a date in the marketing plan.

**Alex Tutor:** Then choose the date by the confidence you need. Sixteen days is roughly even odds: as likely late as early. A date that other work builds on should sit near the top of the range, about 21 working days.

**Sofia:** And the fourteen days from the start?

**Alex Tutor:** That's the sum of the most likely values, 5 + 6 + 3. With a long bad side on two tasks, it's more often missed than met.

> **Exercise:** **True or false:** the sum of the most likely values (14 days) is a safe date to promise for the test.

## Never a single date as a promise

**Alex Tutor:** So the message to Leo carries three things: the expected value, the date you are fairly sure of, and what drives the spread. "Test expected in 16 working days; 21 fairly sure; the questions are the uncertain part."

**Danylo:** And when the estimate changes halfway?

**Alex Tutor:** Re-estimate what is left and report the new range, not "on track". As unknowns get answered, the range narrows. That narrowing is progress too.

**Vira:** Sometimes my honest answer is "I will know in a week".

**Alex Tutor:** That's a fine estimate too: a date by which you'll have a better one. What isn't fine is a number nobody believes.

> **Exercise:** Match each statement about the test to what it really tells Leo.

**Alex Tutor:** Last one: what do you send when the estimate moves halfway?

> **Exercise:** Halfway through, the test questions turn out harder than expected. What should your next update to Leo say?

## Your turn: the estimate for Leo

**Leo:** Fine. Send me the test estimate in a form I can use. Short.

**Alex Tutor:** Three or four sentences: the expected value, the date you are fairly sure of, the main cause of the spread, and when you will update it.

**Danylo:** And please, no "fourteen days" in it.

**Sofia:** Range first, then the date Leo can build on.

> **Exercise:** Write a 3–4 sentence message to Leo with the diagnostic test estimate: the expected value, the date you are fairly sure of, what drives the spread, and when you will update it.

> **Key points**
>
> - A **range estimate** says how much is still unknown; a single number hides it.
> - **Three-point estimate:** expected value E = (O + 4M + P) ÷ 6, standard deviation σ = (P − O) ÷ 6. Keep both: the average alone hides how late the work can be.
> - For several tasks in a row, **add the expected values and add the variances** (σ²), then take the square root. Adding the standard deviations overstates the spread.
> - The expected value is roughly even odds; a date others build on sits near the top of the range (about E + 2σ).
> - Report a range with its confidence and its main cause, and update it as the work moves.

**Alex Tutor:** Next time: every owner pads, and the project date becomes absurd. We'll look at how earlier Klasna launches really went.

- Previous lesson: [Case: the schedule to 1 February](https://productovi.com/courses/project-management-without-bureaucracy/schedule-to-a-fixed-date-case.md)
- Next lesson: [Past projects as a reference, and one shared buffer](https://productovi.com/courses/project-management-without-bureaucracy/past-projects-and-one-buffer.md)

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