Simple Random Sampling Method Example | Steps With Math

You’ll see “simple random sampling” in textbooks and class projects for one reason: it’s a fair way to pick a sample when you can list the whole population. No grouping. No pattern. Just a clean draw.

Below you’ll get a walkthrough, a reusable write-up template, and a checklist you can follow the next time you need to show your method.

Simple Random Sampling Method Example With Clear Steps

Simple random sampling means you select n units from a population of size N so that every unit has the same chance to be picked. If you repeat the process many times, each unit shows up in samples at the same rate.

To do it well, you need a sampling frame: the complete list of units you could pick from, like a class roster or a spreadsheet of IDs. If your list misses people, the draw can’t represent the full population, even if your random tool works fine.

What You’re Trying To Do	Simple Way To Do It	What To Watch
Pick 10 students from 240	Number 1–240, draw 10 distinct numbers	No repeats if sampling without replacement
Sample receipts for an audit check	Use a random number generator on receipt IDs	Keep a log of the draw
Choose survey invites at random	Shuffle the ID list, take the first n	Confirm the list includes all invitees
Pick products for quality testing	Assign numbers, then draw by number	Don’t skip “messy” items
Run a quick class demo	Put slips in a jar and draw	Fold slips the same way
Sample from a spreadsheet	Add RAND(), sort, take the top n	Freeze values before sharing
Make a repeatable sample	Use software with a fixed random seed	Record the seed and date
Avoid biased “grab” sampling	Stick to the draw rule, not convenience	Don’t pick “who’s around”

When Simple Random Sampling Fits And When It Doesn’t

This method works best when you can list the population and you can measure any selected unit without big cost jumps. It can fall apart when the list is incomplete or when a subgroup is tiny and you must guarantee it appears in the sample.

Good Fits

• You have a complete roster or database of the population.
• Units are similar enough that you don’t need subgroup quotas.
• You want a selection rule you can explain in one paragraph.

Red Flags

• Your list excludes some units, like new enrollments or missing records.
• Many selected units won’t respond, and replacements would be hand-picked.
• You must guarantee representation for small groups.

How To Do Simple Random Sampling By Hand

If you can number every unit, you can run a clean draw with paper slips, dice, or a table of random digits. The rule stays the same: pick a repeat-free set of randomly chosen IDs.

Step 1: Define The Population And The Unit

Write one sentence that locks down what counts as “in.” A population might be “all Grade 10 students enrolled on October 1,” and a unit might be “one student.”

Step 2: Build The Sampling Frame

Make the list you’ll draw from, then check for duplicates and blanks. If you find errors, fix the list first and only then draw.

Step 3: Assign A Distinct Number

Give each unit one number from 1 to N. If your list already has IDs, you can use them if each ID maps to one unit.

Step 4: Choose The Sample Size

Pick n that you can actually collect. A bigger n lowers sampling error, but it raises the time you’ll spend gathering data.

Step 5: Draw Numbers Without Steering

Shuffle slips in a jar, roll dice, or use random digits. If a number repeats and you’re sampling without replacement, ignore it and take the next valid new number.

Step 6: Record What You Did

Write down the tool you used, the date, and the final selected numbers. That short record makes the method easy to verify.

How To Run The Draw In Excel Or Google Sheets

Spreadsheets make the selection fast when your population is already a list of IDs. It takes a minute once set.

RAND Sort Method

1. Add a new column next to your IDs.
2. Enter =RAND() and fill it down the full list.
3. Sort by the RAND column from smallest to largest.
4. Take the first n rows and paste values to freeze the sample.

Sampling Without Replacement And With Replacement

In many class tasks, you sample without replacement: once a unit is chosen, it can’t be chosen again. That matches real situations like picking students for a survey or items for inspection.

Sampling with replacement means each draw puts the unit back into the pool. You can draw the same unit twice. The math can be simpler in some lessons, yet in many school surveys it feels odd to contact the same person twice.

A quick rule: if you need distinct units, sample without replacement and skip repeats. If an assignment asks for a with-replacement sample, say that in your method line and allow repeats so your write-up matches your procedure.

Quick Random Digit Table Demo

Number your units 01 to 50. Read two digits at a time from a random digit table. Keep numbers 01–50, skip 00 and 51–99, skip repeats, and stop when you reach your target n.

Worked Sampling Example With Data And Math

Here’s a complete sampling example you can copy. A school has N = 200 students in Grade 10. You want a sample of n = 20 students to answer a short survey for a statistics assignment.

Build The Sampling Frame

You export the roster to a sheet with StudentID and Name. You confirm there are 200 rows and each StudentID is distinct.

Pick A Sample Size With Simple Math

If you’re sampling a proportion and you want a quick target, one common starting formula is:

n0 = (Z^2 × p × (1 − p)) / e^2

For 95% confidence, Z = 1.96. If you don’t know p, many classes use p = 0.5. For a student project, you might choose e = 0.2 to keep the workload realistic. With those inputs, n0 lands near 24. Since the population is finite, a common adjustment is:

n = n0 / (1 + (n0 − 1)/N)

With N = 200, that moves the target down near 21, so n = 20 is a sensible pick for time limits.

At the core, the selection rule must give each unit the same chance. NIST describes a simple random sample as one where each response in the population has an equal chance to be observed (NIST guidance on randomly sampled data).

Run The Selection In A Sheet

You add a RAND column, fill it down 200 rows, then sort by RAND. The first 20 rows after sorting are your selected students. You copy those rows to a new tab and paste values so the list doesn’t change when the sheet recalculates.

Document The Final Sample

You save the selected StudentIDs and note the date and file name. If your teacher asks how you drew the sample, you can point to the exact steps.

Small Tweaks That Keep The Sample Fair

Random selection is only half the job. The other half is how you handle missing responses and unusable records without drifting into hand-picked choices.

Use A Nonresponse Rule Before You Start

If you expect nonresponse, draw a little extra at the start (say 25 for a target of 20), contact in random order, and stop once you reach 20 complete responses. That keeps the contact order random.

Freeze The Sample List

RAND changes when a sheet recalculates. Copy and paste values in a new tab so your sample stays fixed.

Quality Checks For Your Sampling Write-Up

When you write the method section, keep it concrete: population, sampling frame, random tool, and final n. If you want standard classroom wording, Khan Academy shows common ways students generate simple random samples (techniques for generating a simple random sample).

Check	What To Watch	Fix
Frame completeness	Missing units or duplicates in the list	Clean the roster before drawing
Distinct IDs	Two units share one ID, or one unit has two	Assign one ID per unit, then redraw
No hand-picked swaps	Replacing “hard” units with easier ones	Use a prewritten replacement rule
No repeats	Same unit selected twice when you need distinct units	Skip repeats or use shuffle-and-take
Logged steps	No record of how numbers were drawn	Write the method, date, and tool
Frozen spreadsheet values	RAND recalculates and changes the sample	Paste values in the sample tab
Clear unit definition	Mixing students and classes in one list	Choose one unit type and stay with it
Response tracking	Dropping nonresponses with no rule	Contact in random order until n completes

Common Mistakes That Break Randomness

Most “random” samples go wrong in predictable ways. If you avoid these, your method section will read clean and your results will be easier to trust.

• Convenience picks: choosing people who are nearby or easy to contact.
• Pattern picks: taking every 10th name from a list that has a hidden order.
• Untracked redraws: rerunning RAND until the sample “looks right.”
• Quiet exclusions: removing units after the draw because they seem odd.
• Changing the population mid-project: adding units after the draw, then mixing them in by hand.

How To Write It Up In A Report Or Assignment

A solid sampling paragraph is short and specific. Here’s a template you can edit:

“The population was all Grade 10 students enrolled on October 1 (N = 200). We used the grade roster as the sampling frame and assigned each student a number from 1 to 200. We generated random numbers in a spreadsheet, sorted by RAND, and selected the first 20 distinct students (n = 20).”

If you used replacements due to nonresponse, add one sentence that states the replacement rule you followed.

One-Page Checklist You Can Follow

Use this run-through before you submit your work.

• Population statement written in one sentence, with a date boundary if the roster changes.
• Sampling frame saved as a file or sheet tab, cleaned for duplicates and blanks.
• One number assigned from 1 to N, with N recorded in your notes.
• Sample size n chosen and written down before the draw.
• Random method picked and used once for the draw.
• Final selected IDs copied to a frozen list that won’t change.
• Replacement plan written before outreach, then followed without hand-picking.
• The phrase simple random sampling method example used in your method section so the reader knows the sampling type.

Follow the steps, keep a record of the draw, and your sample will be fair, repeatable, and easy to grade, even when someone checks your notes.