When there is wide variation within the groups and less variation from group to group, which is the appropriate type of sampling method?this is a...

There appears to be something wrong with the question. I understand the question is about method of drawing samples from a large population of objects so that conclusion about the complete populations can be drawn based on study and analysis of characteristics of the sample drawn. The objects referred here can be anything for which some characteristics need to be studied. For example, it may be students in a class, or it may be a bags of cement produced in a cement factory.

Frequently, it is possible to achieve required level of reliability and confidence, by identifying separate groups within the whole population and drawing samples from each group, and analysing their characteristics separately. However this approach works only when it is possible to identify separate groups within the population such that there is large variation between the group, but much less variation within the group. For example, for studying the distribution of height and weight of students in a university, it might desirable to divide all the students in two groups based on gender, because the average height and weight of men is higher than that of women. Thus there is large variation between groups men and women, but less variation within each group. The question posed above assumes the opposite - wide variation within the group and less variation across the group. However, we can discuss the nature of sampling method without getting entangled in the question of variation within and across the groups.

When separate groups have been identified within a population there are three broad approaches to sampling. These are:

1. Draw a common sample for the whole population without differentiating without groups. This method may be most appropriate when it is not easy to distinguishing between members of different groups at the time of drawing sample. For example, is a sample is being drawn from a listing that does not identify gender, it is not possible to listing draw separate sample for men and women. However in this method the samples are divided in groups after study of the sample drawn. Also separate analysis is made for each group.


2. Draw proportionate sample from each group based on the total size of the group. For example, if ratio of number of males and females studying in a university is 3 to 2, the sample size from these two groups will also be in same proportion.


3. Draw sample base on expected variation within the group. The sample size needed to achieve a desired level of reliability increases with increasing variation within group. Therefore, larger sample is required from groups with larger variation. This method can be used only when some preliminary estimate of variation within groups are available.

I think it is worthwhile to point out that systematic sampling mentioned in the answer above, refers to another aspect of sampling - the method of identifying the members of the total population picked out for sample study. It has no bearing on the sample size or its composition in terms of groups within the population.