The planning stages.
Getting idea for the exploration is perhaps the hardest part. One of the most useful things we will learn in Mathematical Studies is statistics, it has applications in a wide range of areas, from market research, finance to medicine and identifying global trends or connections. It is very likely that at some stage in your like you will need to conduct a study, some research or present a convincing argument based on some simple statistical results. For that reason we will focus our efforts on learning to write a good one, so what does a statistical study include?

In your exploration you will be asked to compare at least 2 variables, but what does that mean? You could have a little fun here, but it's more important to choose something interesting and realistic. The image on the right (below) is from a website (Thanks @TylerVigen) that shows how some things are correlated, the question is: Is the connection real, or is there causality? Have a look on the site  there are some really strange connections!
The interesting thing is when you pick your variables you will need to investigate them in a way that makes sense. For example with the following two variables we could ask a number of questions.
Size of a person's feet

Weight

"Does a person's foot size affect their weight" or "does a person's weight affect their foot size" or "is their a connection between a person's foot size and weight"
Of course this was a really boring question to investigate, there might be a connection to a point but it will have more to do with your age as a child, then your feet will stop growing and unfortunately for many of us our weight gain continues! As soon as you have the variables you would like to explore, write them down, then share them with others. Have your peers give you feedback on your variables. When your friends show you their exploration question consider asking them the following questions, they are hard questions but if they can be answered then you are well on your way to a good exploration which will bring you meaningful and interesting answers. Questions to ask your friends about their exploration, (my students should click the survey icon and submit your responses):


The introduction.
Once you have you ideas and you are certain you can collect enough data (n=100), it's time to communicate it with "the world". There are a number of times in your careers that you will be asked to submit a proposal, this is kind of the same thing. Here it is important to tell us the what, who, why, when and hows of the study you are about to do. The IB mark scheme says this (right), as you can see it is only worth 2 marks, but they are easy marks to get. There are more marks later on for commitment, at this point if you are able to tell us why you are doing this it might go a long way to convincing us you are committed.

Data Collection
When it comes to criterion B, within the context of a statistical investigation, there are 3 things you need to think about:
Sufficient data is subjective, but I see no reason why you cannot collect 100 pieces of data in your survey, experiment or research. Relevant is not as subjective, but you should ask the questions, or perform an experiment that will give you results to help you answer your question. The moment you have superfluous information you will start to lose marks. You must have a reason to collect your data  make sure you say why you will collect it and then make sure you actually analyze it. Finally it is important that you organize your data into a clear coherent table. Here it is a good idea to use a spreadsheet. 
The Calculations
The calculations are what tell your story. It is really important that in your plan you outline which calculations you will make and why. Of course you must then carry out your own proposal. Each time you make a calculation, ask yourself "why is this useful", for example: why do you calculate the mean? The mean is a very common average to calculate and it is a measure of central tendency, so that you can highlight those above and below this "central" point. Be careful though, all of these measures have their strengths and weaknesses. At some point you will look at the 'connection' between two variables and you should look at the discussion surrounding causation and correlation.
Charts:
Bar Charts & Pie Charts Line Graphs Scatter Plots Box and Whisker Cumulative Frequency Charts Histograms 
Single Variable Calculations:
Mean Median Mode Range Standard Deviation 
Two Variable Calculations:
Product Moment Correlation Coefficient Chi Squared Test for Independence Spearman's Rank Correlation Coefficient Linear Regression 
Telling the story
Think of your IA like a story. It should have an introduction, a middle and a conclusion. No one section is more important, each has it's own part to play. Hans Rosling tells a brilliant story using statistics, but we must do it in writing  we need to convince our audience we have realized something The reader must be guided through what they are reading, right the way from the title to the final conclusion. The basic structure goes something like this:

You will find many IA checklists online  I found this one on the first hit of a google search. It should guide you in your writing, but it is probably not the best choice for headings and structure  but do make sure you cover all the points.
