ریاضی
Population and Sample
The population is everyone you want to know about; the sample is who you measure. One school survey showing which numbers are known and which are estimated.
Population and sample
The population is every member of the group being studied; a sample is the smaller part of that group which is actually measured.
- دیگر نام
- Census and sample
- طلبہ کہاں پڑھتے ہیں
- Grade 7 in data handling, and again at GCSE and IGCSE in the sampling questions that usually open a statistics section.
مختصر جواب
The population is everyone or everything you want to know about; the sample is the part you actually measure. In a school of 900 pupils, the population is all 900. If you ask 60 of them how they travel to school, those 60 are the sample, and their answers are used to estimate the school's.
ایک مثال
900 pupils (population) → 60 asked (sample) → 36 walk → estimate 60% of the school, about 540 pupils
Three of these numbers are known and one is not. The school has 900 pupils, 60 were asked, and 36 of them said they walk: all counted, all certain. The claim that about 540 pupils in the school walk is none of those things — it is an estimate produced by scaling up the sample, and it would come out differently if a different 60 had been asked.
Which numbers are known and which are guessed
The difference between the two words is not really about size. It is about which figures you are entitled to state as fact. Anything measured inside the sample is known: 36 out of 60 walked, and that is 60% of the sample, exactly. Anything claimed about the population beyond the sample is an estimate, however careful the method.
Keeping the two apart is most of what these questions test. A statement like "60% of the school walks to school" is really "our best estimate is that about 60% of the school walks", and an exam answer that says the first when it means the second is claiming more than the data supports. The vocabulary exists so that the difference can be stated: a figure about a population is a parameter, a figure about a sample is a statistic, and a statistic is used to estimate a parameter.
Asking everyone has a name
A survey that covers the whole population is a census. Pakistan runs one nationally, a school runs one every time it takes a register, and the appeal is obvious — no estimating, no uncertainty about who was left out.
The reason samples exist at all is cost, time and, sometimes, destruction. Asking 900 pupils takes fifteen times as long as asking 60. Testing every match in a factory to check that it lights would leave nothing to sell. A well-chosen sample of 60 answers the question well enough to act on, at a fraction of the effort.
That trade puts the weight on how the sample is chosen rather than on how large it is. A carefully chosen 60 gives a better estimate than a carelessly chosen 300, because a bad method does not get less biased when it is repeated more times.
The question decides the population
The population is not a fixed thing about the school; it is defined by what you are asking. If the question is about how Year 11 revises, the population is Year 11, and a sample drawn from the whole school is answering a different question. If the question is about the city's schools, one school is itself only a sample.
Students lose marks here by naming the population as "the students" when the question was about students who take the bus, or about parents. Write down what you want to know first, in a full sentence, and the population is whoever that sentence is about.
عام سوالات
How big does a sample need to be?
Big enough to be worth scaling up and chosen well enough to represent the population, which is the harder condition. School questions usually specify the size, and a rough rule for coursework-style tasks is at least 10% of a small population. Doubling the size of a biased sample does not improve the estimate at all.
What is the difference between a parameter and a statistic?
A parameter is a number describing the whole population, such as the true percentage of the 900 pupils who walk. A statistic is the same kind of number calculated from a sample, such as the 60% found among the 60 asked. Statistics are known and used to estimate parameters, which usually are not.
Why not just do a census every time?
Because it costs time and money, and sometimes because measuring destroys what is measured — you cannot crash-test every car. A census also takes long enough that the answer can be out of date by the time it is finished. A sample gives a usable answer quickly, and the uncertainty it carries can itself be estimated.
Can a sample ever be the whole population?
If it is, it is a census, not a sample. The distinction matters in the wording of exam answers: with a census there is no sampling error to discuss and no need to talk about representativeness, so a question that offers you a census is testing something else — usually cost or practicality.
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