[Maths Class Notes] on Sample Size Pdf for Exam

The sample size is a measure of the number of individual samples that are present or have been observed during an experiment or a survey conducted. To understand it a little better, we can take an example. If we test 100 plants for a certain type of disease-causing virus, the sample size is 100. To carry out the survey, you received a 30,500 complete set of questionnaires, then the size of the sample is 30,500. The sample size in statistics is represented by the letter ‘n.’ Hence, the Sample Size definition is a measure of the number of samples for a particular study or research.

 

Factors Contributing To Sample Size Collection

There are certain factors that are taken into consideration before determining the sample size of a particular experiment or a study. These are-

• Size of the Population– The size of the population that is being studied is the first thing that is considered. The study that involves the conclusion from a larger area says an entire country will require a larger sample size in comparison to studying that includes smaller areas like a state or a city. The margin of error- Is another thing that is considered. Given the fact that the data that has been collected is accurate to what extent? There are high chances of errors in the data, so the margin of error is always considered.
  

• Standard Deviation – Standard deviation refers to the amount of deviation seen in the individual sample and the whole group of samples. Let’s say, for example, if the samples of soil are collected from a park, they are likely to show lesser deviation in the amount of nitrogen content in them, as opposed to the samples of soil that have been collected from across the nation.
  

What Dangers Are Related to Small Sample Size?

It has been said that the smaller size, the more accurate the findings!/Let us understand this by an example. A team decided to study how many people exercise daily in a country and what they did was pick up 5 people and interviewed them regarding the same. Two of them said that they exercise regularly. The outcome of the study would be that 40% of the population exercise regularly, and this would represent the country as a whole. The data does carry a lot of inaccuracy, and the Margin of error is quite high. So smaller the sample size, the higher are the margins of error and vice versa. Hence, it is advisable to select a large sample size to conduct any given experiment or study.

 

Calculating the Sample Size

To calculate the size of the sample, the figures you need are- Desired confidence level, margin or error, the total number of people in the population. There are two sample size formulas-

1. Sample Size Calculation is Done In the Following Manner

Sample size can be calculated by (Percentage Distribution of 50)/ (?percentage of Margin of error/ Score of confidence level) squared)

      2.  Finite Population Correction-

True Sample is equal to –(Size of sample*Population)/ (Size of sample+Population-1)

Understanding the concept of Sample Size better

 

The Sample Size examples would let us understand the concept even better. So here is one

 

In a given society the height of its residents is normally distributed at a standard deviation of 5 inches. Then, how will we find the minimum sample size required to construct a case study with the confidence level being 95% and the margin of error being 0.5 inches.

The formula to determine the sample size is, n= ({Z_α/2σ}/E)²

 

Where, E= 0.5 inch σ = 5 and α = 1 – 0.95 = 0.05

 

Hence, Z_α/2 = Z 0.025 = 1.96

 

n = ({Z_α/2σ}/E)²

 

Putting the values, we get

N = ({1.96(5)}/0.5)²

 

Which comes out to be 384.16 and if we round it off, it is 385.

 

Conclusion

Not only a small sample size, but even the larger one is a problem. The interpretation with such large samples makes it difficult for the research and also affects the figures. Hence, it is not recommended to take larger samples. A moderately good amount of sample is what should be taken in order to obtain accurate results. Though there is no specified limit to decide the sample size there are a few thumb rules that can be followed. One of them says a minimum of 30 samples should be taken, and another says 12 minimum samples should be considered before carrying out a study.