## Within the limitations imposed for particular cases, the under-lying principle of most sampling methods is the selection of a random sample, free from bias and therefore truly representative of the population.In this type of sample, every individual in the population has an equal chance of being included in it. The number in the sample must be sufficiently large to include all the variations of the individuals in the population. A very variable material will need a large number in order to obtain true representation.Numerical sample:The sample in which all the fibres in the population have an equal chance of being represented is called a numerical sample.Thus the expressions random and numerical sample may be interpreted in the same way when we select the sample of the fibres.In the numerical sample, the proportion by the number of the long medium and short fibres would be the same in the sample as in the population. For example, in bulk, there should be 4 million long, 10 million medium, and 1 million short fibres in a perfect numerical sample. This perfection is almost impossible so that a random sample with its corresponding random error is the type of sample with which we normally operate.Sample:The sample for textile material testing is a relatively small fraction that is selected to represent a population. The  reasons for only testing samples are:1 - Time required per test 2 - The destructive nature of many of the testsHow a small sample can be in relation to the population? We can understand it by the below example:Weight of cotton bale = 500 lbs                                   = 500 x 453.6 grams                                   = 500 x 453,6 x 1000 mgs.                                   = 226800000 mgs.Sample weight            = 20 mgs. ( for testing of the staple length)Now we calculate the ratio between sample weight to bale weightSample to bale weight ratio = ( 20/226800000)                                            = ( 1: 11340000)Here we can see that less than one eleven millionth of the bulk material represents the bale.There are many factors those influence the sampling methods up to large extent.1 - The form of material2 - The amount of material available 3 - The nature of the test4 - The type of the testing instrument5 - The information required6 - The degree of accuracy requiredWithin the limitations imposed for particular cases, the under-lying principle of most sampling methods is the selection of a random sample, free from bias and therefore truly representative of the population.In this type of sample, every individual in the population has an equal chance of being included in it. The number in the sample must be sufficiently large to include all the variations of the individuals in the population. A very variable material will need a large number in order to obtain true representation.Numerical sample:The sample in which all the fibres in the population have an equal chance of being represented is called a numerical sample.Thus the expressions random and numerical sample may be interpreted in the same way we select the sample of the fibres.In the numerical sample, the proportion by the number of the long medium and short fibres would be the same in the sample as in the population. For example, in bulk, "there should be 4 million long, 10 million medium, and 1 million short fibres in a perfect numerical sample". This perfection is almost impossible so that a random sample with its corresponding random error is the type of sample with which we normally operate. 