Saturday, September 17, 2011

Quartiles, deciles and percentiles

I have an affinity with Mathematics. This is a short blogpost consolidated from some quick google and my little explanation on how to remember coupled with my little list of related topics.

Quartiles, deciles and percentiles (which are all examples of quantiles) are standard descriptive statistics which are used to divide a set of data points into equally sized subsets.

Quartiles divide the sample into four groups, with the lower quartile being 25%, the median value being at 50% and the upper quartile at 75%. Quartiles are essentially ranking mechanisms. The upper quartile is that position in the data set which has 75% of values below it and 25% above it. (How to remember: Quartile comes from the word quarter).

Deciles divide the sample into ten groups, with the lower decile is equivalent to the 10th percentile. (How to remember: Decile comes from the word decimal).

Percentiles divide the sample into one hundred groups. The 90th percentile is that position in a data set which has 90% of data points below it, and 10% above it. (How to remember: Percentile comes from the word percent).

So what is interquartile range?
Ans: 75th percentile - 25th percentile

Other related topics:
- Cumulative frequency curve
- Normal (or "bell-shaped") distribution.
- Power-law distribution - this is interesting. It looks something like a hockey-stick leaning against the y-axis. It appears to situation where big is rare and small is common. The distribution of wealth is one example, there are many poor souls around but few very, very wealthy ones.

When we are analysing data, we need to be mindful if it is one of power-law distribution. 'cos we are schooled to think that normal distribution is well, normal.

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