Statistics for Non-probability sampling

Hi! I need help with regard to the appropriate statistics to be used on a non-probability sample.

I did a study on YouTube users. Since, there is no data of how many YouTube users there are, I did a purposive sampling for my study.

I reported the data using descriptive stats (measures of central tendency) but some of my professors want me to account for variances.

From what I've researched so far, measures of variances are not appropriate for non-random samples. The SPSS application also assumes random sampling only.

Can you help me with this? I've researched everywhere including stats book but couldn't find an answer. I admit I'm a qualitative researcher, but I've been trying my best to grasp statistics. Thank you.
your sampling method must always be selected to reflect the population accurately; simple random samples are not required, but if you're sampling in an obviously biased fashion, your professors have a duty to stop the analysis before conclusions are drawn :D. Can you elaborate more on your sampling methods and research goals?
Hi, thanks for your replies. I used purposive sampling in a survey I conducted among YouTube users. I couldn't do simple random or any probability sampling methods because there was no way for me to know:

1.) exact number or estimation of the YouTube population
2.) there was no list whatsoever of YouTube users

Basically, what I used was purposive and snowball.

The study is exploratory.

So, how do I account for variance?