The problem with averages: a tale of two school systems

The problem with averages

Let me start with a fundamental lesson from any introductory statistics class. An average tells you about the center of a distribution, but it may tell you very little about the actual experiences of most people in that distribution — especially when those people are clustered far from the average, either above or below it.

Even if officials argue that all student groups showed improvement, we must examine the rate and magnitude of these improvements. Consider what happens when there are two distinct groups with very different performance levels (bimodal distribution). If high-performing White students improve by 5 points while lower-performing Black students improve by just 1 point, the achievement gap actually widens despite 'improvement' for all.

'Improvement across all groups' can still represent a failure of equity. The crucial metric isn't whether all boats rise — it's whether the distance between them is shrinking.

Mayor Bowser's recent announcement about DC CAPE results provides a textbook example of this statistical sleight of hand. The statement celebrates that 'almost all student groups improved' and emphasizes 'the largest increase in proficiency rates made since the pandemic.' But buried in a single sentence, the Mayor acknowledges that 'differences in proficiency among student groups by race/ethnicity persist.'

This is precisely the problem. The statement treats persistent achievement gaps as a minor footnote rather than the central crisis. Notice what the announcement conspicuously avoids:

• No data on whether achievement gaps are closing or widening
• No discussion of the magnitude of improvements by racial group
• No acknowledgment that DC has some of the largest achievement gaps in the nation

The Mayor's statement mentions that economically disadvantaged students improved by 3 percentage points in ELA while students with disabilities improved by 1.6 percentage points. Where are the racial comparisons? True progress would mean faster improvements among struggling students, actively closing the gap. Instead, this statistical sleight of hand allows officials to present 'improvement' while avoiding the harder conversation about whether educational disparities are being eliminated.

NAEP data: the gap persists despite 'all boats rising'

The NAEP data tells this story with devastating clarity. Looking at 4th-grade reading scores in DC from 1992 to 2024 — a span of over three decades — we see exactly the phenomenon I'm describing. The achievement gap between White and Black students remained staggering at 62 to 68 points over 32 years — with only a modest change that officials overlook while celebrating overall progress.

• White students started high and remained high
• Black students started much lower and remained much lower
• The gap between them grew despite decades of 'improvement'

Source: nationsreportcard.gov/dashboards/achievement_gaps.aspx

DC's education system is a textbook example of a bimodal distribution where virtually no students perform near the 'average' the officials celebrate. Students are clustered near either the White student circles or the Black student plus signs on the graph, creating two distinct populations with a vast gulf between them. The 'average' represents an imaginary point where most students don't exist.

The right statistic: the size of the achievement gap

Here's what DC officials should be measuring, and what education researchers should be demanding they measure: the size of the achievement gap. This is the most critical statistic facing any education leader in a city like Washington DC.

When White students at the top of the achievement distribution gain ground, that's worth acknowledging — but these students were already positioned for success with access to college pathways and advanced coursework. Their marginal improvements, while positive, don't fundamentally alter their life trajectories. Now consider what happens when we focus policies and resources on students furthest behind. When they make even modest gains, the impact is transformative — changed lives, expanded opportunities, strengthened communities.

The elephant in the room: segregation

The people who lead DC education know this. They understand statistics, they understand achievement gaps, and they are aware that the picture is grim. This failure is predictable because of our refusal to acknowledge the most important education policy problem facing Washington DC and other major Northern cities: school segregation.

Segregation is a word we don't like to say in the historic North. It doesn't belong to us, we tell ourselves — it belongs to the South. But based on educational outcomes, segregation belongs to us far more than it ever belonged to the South. Our segregation is more complete, more absolute, and more devastating in its effects.

In my own research I demonstrate how segregation is a root cause of numerous problems in our system, all of which contribute to these achievement gaps we fail to address. In segregated school systems, wealthy parents concentrate their resources — both financial contributions and volunteer time — in schools serving predominantly White, affluent students. Meanwhile, schools serving predominantly Black students lack access to these crucial supplemental resources. This isn't about residential patterns; this is about policy choices that maintain and exacerbate segregation.

DC has only a handful of truly diverse schools where Black and White students, rich and poor, and students with and without learning disabilities learn together. In the rest of the system, these groups attend separate schools. We need to study these diverse schools — some of which are charter schools — and learn from their successes. We need to engage in an actual desegregation program.

To those who claim this is all a residential problem: visit schools such as Cardozo High School, Roosevelt, or Eastern. You'll find segregated schools sitting in diverse neighborhoods. The segregation isn't accidental — it's the result of policy choices about school boundaries, school choice systems, and resource allocation.

It is our obligation as researchers to tell the truth, even when — especially when — that truth disrupts comfortable narratives of progress.

DC education fails specific groups of students in a very nonrandom way. The fact that average performance improved cannot and does not change this fundamental truth. Until DC officials — and the education research community — are willing to name segregation as the core policy problem and commit to desegregation as the necessary solution, we will continue to see press conferences celebrating averages while the vast majority of DC students remain underserved.