Question

What are some situations in which you could be mislead by considering only an indicator of the average--whether it was the mean or the median--and failed to take into account the variablity (Standard Deviation). Are there any claims you see in the media that are questionable based on the N included in the data?

Answer 1

If we rely solely on the measures of central tendency, without considering the dispersion of the data, we are likely to make incorrect assumptions about the data. Dispersion measures speak of the reliability, or dependability of the average value of a series. They also enable the statisticians for making a comparison between two or more statistical series with regard to the character of their stability or consistency. Futhermore, theyfacilitate in making further statistical analysis of the series through the devices like co-efficient of skewness, co-efficient of correlation, variance analysis etc.

The N represents the sample size of a study. The larger the sample size, the greater are the chances that the results of the study can be generalised. In several claims made by the media, the sample size or N is extremely small. And yet, these statistics are presented as though it accurately applies to the entire population. This cannot be true because these small sample sizes are likely to yield highly biased results.