Mean

• There are three things calculated from the sample: mean, variance and functional form. The mean is the average, that is, the data in the sample added together and divided by the total number in the sample. If the sample is too small, this mean will be inaccurate and not reflect the true mean in the data or population studied. If a study looks drug side effects, but takes a small sample size (for example, 10 patients in a 2,000-patient study), the mean of how often the side effects happen won't represent how often they really happen.
  
  

Variance

• If the sample size is inadequate, the variance will also be affected. Variance is used to tell how the population or data spreads out --- its distribution. For example, in the drug side effect study where only 10 patients were sampled out of 2,000 patients, the distribution of side effects would not accurately reflect the occurrence and percentage of side effects occur outside the mean.
  
  

Functional Form

• If this graph was based on an inadequate sample size, it could mean a drug that causes sever side effects could get put on the market..graph grid green image by Nicemonkey from Fotolia.com
  
  The functional form of the data or population studied --- that is, how the data looks when graphed --- can also be skewed by inadequate sample size. By looking at the graph, theories and opinions will be formed that are not accurate. If a graph from the drug study where only 10 patients were sampled showed the drug had almost no side effects, then people would be more inclined to consider taking this drug. However, perhaps 1,500 patients actually got severe side effects, such as paralysis. You would never know just by looking at the data taken from an inadequate sample size. If any study is based on inadequate sample size, the research and the implications derived from that study will be inaccurate and may not reflect the negative or positive aspects of the study.