## Descriptive Statistics – starting with the data

September 27, 2013

There are the kinds of analysis that you can do when you start with any data set. This may be the starting point of all data science projects and it will give insights about the data. This is essential for both statisticians and also for consumer of statistical reports.

For quatitative variables :

1. minimum, maximum
2. median, quartile, inter quartile rang
3. box plots
4. mean
5. spread of the data – standard deviation – sometimes there may be gaps in the data when we plot it as a histogram – outliers. When there are underlying special rules in the way the data is being generated, then there will be outliers in the data. For example : Some football clubs can play foreign players salaries above the salary cap, this will produce outlier salaries for those players. Another example : the top deal or product in an ecommerce site, gets the highest clicks by virtue of its position. This will create an outlier if ctr is considered, if the deals are ranked. Cleaning the data is an important first step in any statistical analysis. It is important to understand the reasons behind the outliers. In some cases, it is good to remove the outliers and in some cases it is not so good as we might lose valuable data signals. It is not unusual to report findings both with and without outliers.
6. shape of the data – histograms
7. skewed vs non-skewed, symmetric vs non-symmetric
8. left skewed or negatively skewed – where it has a long left tail – mean < median < mode – the difference between the 3rd quartile and the median is smaller than the difference between the 1st quartile and median
9. right skewed or positively skewed – where it has a long right tail
10. extreme values or outliers – sometimes the data has a much better uniform shape when the outliers are removed

For categorical variables

1. bar charts
2. pie charts
3. Examining the relationship between a quantitative variable and a categorical variable involves comparing the values of the quantitative variable among the groups defined by the categorical variable.

Missing Values

We must understand why the data for some of the variables are missing and the fact that they are missing might bias the result of our work.