Question

Is the randomness of a sample important to statistical data collection? Data analysis?

Why or why not for both of the above?

How about two real world examples?

Answer 1

statistical data collection

suppose when you are calculating the average income of your town or city if you take a particular part of your city for the survey it will give weird results

assume that u have taken a sample of incomes from the developed part ignoring the underdeveloped part then your average will be biased and it is no where near to the income of underdeveloped part and vis versa

so if you choose the sample randomly u will get better results

data analysis

in finding the significant difference between two means if we do not assume the mean to be random then test statistic under null hypothesis does not follow standard normal(large sample) or t distribution(small sample)

so randomisation is essential in both cases