Random Samples & Representative Data
Aligned to 7.SP.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
A sample is a part of a whole population. A random sample, where every member has an equal chance of being chosen, tends to represent the population well. Biased samples can give misleading results.
Worked examples
Example 1
To learn the favorite sport of 900 students, surveying only the basketball team is biased. Randomly drawing 60 student IDs gives a representative sample whose results are more trustworthy.
Example 2
Asking about library hours by surveying people already inside the library is biased — you will never hear from people who do not go.
Example 3
Bigger is not automatically better. A random sample of 100 beats a self-selected online poll of 10,000, because the poll only hears from people who chose to answer.
Practice questions
- A reporter surveys people leaving a gym about their exercise habits. Why is this sample biased?
- Describe one way to choose a random sample of 50 students from a school of 800.
- Why is a larger random sample usually more reliable than a very small one?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Muestras Aleatorias y Datos Representativos
Una muestra es una parte de toda una población. Una muestra aleatoria, donde cada miembro tiene la misma probabilidad de ser elegido, tiende a representar bien a la población. Las muestras sesgadas pueden dar resultados engañosos.
Ejemplo 1: Para conocer el deporte favorito de 900 estudiantes, encuestar solo al equipo de básquetbol está sesgado. Sacar al azar 60 números de estudiante da una muestra representativa cuyos resultados son más confiables.
Ejemplo 2: Preguntar sobre el horario de la biblioteca encuestando solo a quienes ya están adentro está sesgado — nunca oirás a quienes no van.
Ejemplo 3: Más grande no es automáticamente mejor. Una muestra aleatoria de 100 vence a una encuesta en línea autoseleccionada de 10,000, porque la encuesta solo escucha a quienes decidieron contestar.
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