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Just before his report on racial and ethnic disparities was published, Tony Sewell was interviewed and asked a few challenging questions.

He quickly shut them down.

"If you look at our data," he said, before explaining how it showed a "disproportionate number of black people going to non-research universities".

"We've looked at the data," he said later, "and at the very specific ways in which ethnic minorities are doing well".

And a moment later: "We've got data to show under 30-year-old ethnic minorities are doing well in the workplace."

He was at pains, in other words, to point out that the report would be grounded not in vague catch-all statements but in cold, hard data.

The problem with data, of course, is that all too often it is not cold and hard: it is alive, it is supple and it isn't quite as definitive as it first looks.

It is certainly true to say that much of the data on education tells a very promising story about narrowing ethnic attainment gaps.

And one of the best things about the Commission on Race and Ethnic Disparities' report is that it does include some serious, thoughtful data analysis about how well students of different ethnic backgrounds are doing in schools around the UK; the story much of these data tell are indeed quite encouraging.

Look at the mean score for grades for students and adjust them for socio-economic status and you find that actually the best performing students are Bangladeshi and Indian students, that white British pupils are the second worst performing, and that the story for black students is actually far more complex than any single number can tell you.

While black Caribbean pupils are the worst performing, with even lower grades than white British pupils, black African students do better than white British, more or less in line with the average.

But then look at other data points and they tell a different story. Look at charts on excluded pupils and even after you adjust for other factors, black Caribbean pupils are nearly twice as likely to be excluded as white British children.

Still, the report underlines an important message, albeit one that won't be entirely fresh for anyone who has looked into this topic: the reality is actually quite different from (and significantly less depressing than) the conventional wisdom.

And that is also mirrored in some, if not all, of the employment data.

Take the pay gap between different ethnic groups.

After you adjust for other factors like where people live, their degree level and so on, the gaps are far smaller than you might have thought.

And actually white British workers are towards the bottom, not the top of the income spectrum.

Except that this doesn't go for all jobs. Those of ethnic minorities are disproportionately represented in the NHS but disproportionately underrepresented in the civil service - especially the top rungs.

And while the report makes much of a chart showing that in 2020 the proportion of black Caribbean workers in employment rose above white British workers (and all other ethnicities) for the first time since the early 1980s, the chances are that this is a data defect because collection of employment statistics has been thoroughly challenged during the pandemic.

In other words, while much of the data is encouraging, some of it isn't altogether reliable.

The data on pay gaps suffers from small sample sizes and it's hard, frankly, to work out the extent to which these reflect company structures and other factors rather than their attitude to ethnicity.

The overarching message from the report is that actually class and poverty are far more important determinants of people's prospects than ethnicity. And in this it is probably right.

The problem is that having said that it certainly doesn't follow that ethnicity is not a factor. It surely is: why else would there still be such big disparities in many measures of attainment and status even after you adjust for class and poverty?

Nor is presenting a ream of data points about ethnic minorities' educational attainment the same thing as disproving the notion that there are historical, structural and systemic forces which perpetuate ethnic inequalities.

This, perhaps, is the real problem with the report.

There is plenty of hard, chewy analysis. Read it via the charts alone and you're left with a somewhat encouraging picture of Britain's social fabric, but with plenty of worrying provisos (for instance, stop and search stats, or the unnervingly universal extent to which police forces around the country underrepresent the ethnic minorities in their areas).

The recommendations themselves are both sensible and pretty uncontroversial.

But read the text alone and you're left with a different impression.

Gone is much of the nuance - and paragraph after breezy paragraph makes grand assertions that aren't really data-led.

We are told to: "Consider the greater presence of ethnic minorities in the current government and opposition, this time occupying top positions such as Chancellor of the Exchequer, attorney general, business secretary and home secretary."

There are complaints about "linguistic inflation on racism" and "strident anti-racism".

Perhaps it's unsurprising that the biggest complaints about the report have concerned not the deep analysis and the recommendations, but the commentary that sits on the page alongside them.

But while Tony Sewell urged us to "look at the data", both parts matter.