Explain the results and meaning of these measures in your report. Include a summary of the data in your report using a graph or table. Use Excel for this task.
Answer:
Introduction:
The given data has the following measures of central tendency- mean equal to 3.277, median at 3.06 and a low mode of 1.39. Each one has its own merits and demerits. Let
us focus on mode and mean.
Mean is the most commonly used measure of central tendency. It can be used for further mathematical treatment , but suffers from the problem of getting affected by extreme values. It is also more cumbersome to calculate than other measures.
Mode is a simple measure that is unaffected by extreme values. But it can be undefined in some cases and cant be used mathematically any further.
As the diagram shows clearly this data will be positively skewed, as Mode < Mean. A mode is not useful in this sense but it helps to see the peak in any distribution. It can be easy to find, unlike mean which takes more time. Mean is also influenced by extreme values, unlike mode which remains unaffected by them. The positive skewness is confirmed by the value of 0.6315 for skewness in the descriptive statistics.
Variability can be measured by different measures- variance, standard deviation( which is square-root of variance), range and coefficient of variation. The first three are absolute measures, and are affected by the units of measurement. The last one –coefficient of variation is a relative measures and is calculated as standard deviation/mean. Its advantage is that it is unitless. (Anon., n.d.). But a problem is that this measure can only be used for non negative values of mean. (Abdi, 2010)
This value for our data equals 1.617/3.277 = 0.4934. if we look at range, defined as = maximum- minimum, we get 8.42-0.65 = 7.77. This looks high as compared to CV. But this comparison is not correct as range is a measure with units and CV has no units. It is always best to use CV as it is a relative measure.
References
Abdi, H., 2010. Coefficeient of variation. In N. Salkind, ed. Encyclopedia of Reserach Design. California: Sage.
Anon., n.d. FAQ: What is coefficeint of varaition? [Online] Available at: HYPERLINK "https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-is-the-coefficient-of-variation/" https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-is-the-coefficient-of-variation/ [Accessed 1 June 2017].
