World Statistics Day is observed by the United Nations every five years on 20 October. It is a reminder of how much we depend on data to understand the world around us.

Statistics help governments measure progress, businesses evaluate performance and ordinary people make sense of the information they encounter every day.

Yet, even with the confidence that I understand stats, I have noticed how quickly I become convinced when an argument comes with a number. 

An opinion might invite me to disagree, but a percentage, a graph or a neatly calculated average makes me pause. It feels as though someone has done the thinking for me and arrived at an objective conclusion. Surely, a number is harder to manipulate than an opinion. 

Except that it isn’t always. And the more I think about it, the more interesting the problem becomes. We spend so much time arguing about whether a statistic is true that we sometimes forget to ask whether it proves what we are being told it proves.

Imagine seeing a company advertise an average salary of Tk52,000. I might assume that working there would offer a reasonably comfortable income, particularly if I were entering the job market. 

But suppose four employees earn Tk 20,000 each while one senior executive earns Tk 180,000. The average salary is still Tk 52,000. The calculation is correct, but it gives me a very different impression from knowing what most employees actually earn.

Nothing in this example requires a fabricated statistic. The problem lies in what I assume the number represents. 

I think this is where our trust in numbers becomes a little dangerous. We tend to treat statistics as finished answers when they are often only partial descriptions.  

Adding a percentage can make that conclusion even more persuasive. Imagine being told that a certain risk level in an investment opportunity or a clinical surgery has fallen by 50 per cent. My immediate reaction might be to consider that a substantial improvement. But if the risk has fallen from two people in every 10,000 to one in every 10,000, the relative reduction is 50 per cent while the absolute or real reduction is one person per 10,000. 

Both descriptions are mathematically correct. However, Neither should be considered in isolation if I want to understand what the change actually means.

This matters because we respond to the sound of a statistic before we have fully understood its meaning. 

By the time we ask what is being counted, we may already have decided what the number means.

The same thing happens when numbers enter public debates, advertisements or arguments about an institution’s performance. 

Someone chooses a favourable period, highlights the measure that improved, or compares a figure with a baseline that makes the change look impressive. Another person might choose a different period or a different measure and tell a less flattering story using the same set of data. 

This is also how a statistic can be used to support a conclusion that the full evidence does not justify. 

A report may contain genuine findings while drawing a much broader conclusion than those findings can support. Looking only for invented numbers will not help us recognise every misleading argument, because misleading presentation does not always require false data.

What makes this harder is that we are not neutral readers. I am more inclined to welcome evidence that supports what I already believe and more likely to scrutinise evidence that challenges it. I suspect most of us recognise this habit, even if we do not always notice it in ourselves. 

Perhaps the most useful statistical habit is to apply the same scrutiny to the numbers we like as we do to the ones we dislike. 

Who has been counted? What is the figure being compared with? What information has been left out? And does the evidence actually support the conclusion, or does the conclusion simply fit what I wanted to believe? 

Questions such as these are helpful when diagnosing the lies our politicians tell us or interpreting data spewed by renowned international organisations.

A statistic can be the beginning of a very useful explanation, but it is not the explanation itself.