--- title: "Stratified Sampling" description: "Work out how many to take from each group so that a sample matches the proportions in the population, and round the results sensibly." canonical: https://lightmysky.com/learn/mathematics/stratified-sampling-mt_CWzOOk0609 source: https://lightmysky.com/learn/mathematics/stratified-sampling-mt_CWzOOk0609.md retrieved: 2026-09-02 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Stratified Sampling Work out how many to take from each group so that a sample matches the proportions in the population, and round the results sensibly. Subject: Mathematics · Area: Data & Statistics · Ages 14 to 15 Page: https://lightmysky.com/learn/mathematics/stratified-sampling-mt_CWzOOk0609 ## Ready when they can - Work out each group's share of the population before sampling - Calculate how many to sample from one group for a stated sample size - Say why the numbers may need adjusting after rounding ## Lesson: Giving Each Group Its Share of the Sample Last stop the fix was a list and a generator: number all 900 members, let chance pick 60. Every member gets the same chance, and that is fair. It can still land oddly. One draw might come back with four volunteers when twelve is their share, because chance cannot read the membership list. Stratified sampling settles the shares first. Split the population into groups that do not overlap and leave nobody out, called strata, and one of them is a stratum. Then decide how many places each group gets before a single person is picked. *(drawing: The three groups are different sizes, so a sample that matches the site gives them different numbers of places.)* A group's share of the population is the group's size divided by the total. Multiply that share by the sample size and you have the group's places. A group of 240 out of 900 has a share of 240 / 900, so in a sample of 60 it gets 240 / 900 x 60 = 16 places. The same sum works the other way round: 60 out of 900 is 1 in 15, and 240 / 15 = 16. It runs backwards: 32 park places from 480 members is 1 in 15, so the sample is 900 / 15 = 60. **Example.** Wren Lane has 240 plot holders, 180 volunteers and 480 park members, 900 in all. For a sample of 60 the three sums give 240 / 900 x 60 = 16, 180 / 900 x 60 = 12 and 480 / 900 x 60 = 32. Check the total: 16 + 12 + 32 = 60. A second check: the groups sit in the ratio 4:3:8, and 16:12:32 is that ratio times four. A group with more places than its share is over-represented, and none is here. *(drawing: The site in fifteen dots: four plot holders, three volunteers, eight park members. Multiply every group by four and you have the sample of 60.)* Real numbers rarely divide so kindly. Take the same three groups for a sample of 50. 240 / 900 x 50 comes to about 13.3, 180 / 900 x 50 is exactly 10, and 480 / 900 x 50 is about 26.7. Nobody can ask part of a person, so round each to the nearest whole number: 13, 10 and 27, which totals 50. Round both decimals up instead and you get 14, 10 and 27, which is 51. Rounding pushed the 13.3 furthest, so pull it back to 13 and the total is 50 again. Round, add up, adjust. Two things stratifying does not do. It fixes the shares of the groups you chose to split by and nothing else, so a difference you never thought of can still be missing from the sample. And somebody still has to pick the 16 and the 12 inside each group. If that picking happens at the Saturday gate, the bias from last stop walks straight back in. Strata earn their keep when the groups tend to answer differently, so splitting by something unrelated to the question just gives you groups that are copies of each other. **Recap.** A group's share is its size divided by the population, and that share times the sample size gives the group's places. Add the places up to check they make the sample size, and compare the ratio with the population's. When the division leaves a decimal, round each group and then fix the total. Stratifying sets the shares; picking at random inside each group is what keeps them honest. ## Practice 24 questions on this page, each with its working shown. ## Needs first - [Populations, Samples and Bias](https://lightmysky.com/learn/mathematics/populations-samples-and-bias-mt_c7knRZy3Vt) - [Ratio Notation and Relationships](https://lightmysky.com/learn/mathematics/ratio-notation-and-relationships-mt_yK51ZnKA8m) ## Opens up - [Averages from Frequency Tables](https://lightmysky.com/learn/mathematics/averages-from-frequency-tables-mt_5WF_Rhdb1X)