Explaining Data Simply

Introduction

Welcome to the fifth and final lesson of Comparing and Communicating Distributions! By now you have a powerful analytical toolkit at your fingertips: you can pair the right summary statistics with a distribution's shape, catch hidden structure that single summaries miss, describe an individual distribution thoroughly, and compare two distributions element by element using specific numerical evidence. That is a seriously impressive skill set. This lesson brings everything together around one last and very practical question: who will read your comparison? In most professional settings, the person who needs your analysis is a manager, a client, or a teammate who has never taken a statistics course. If our well-structured comparison is packed with terms like "right-skewed," "IQR," or "standard deviation," the reader may nod politely and then set the report aside. Our goal today is to write comparisons that remain just as precise as before while being fully understandable to someone with no statistics background.

Why Your Audience Matters

6.0

Replacing Jargon with Plain Language

6

Statistical term	Plain-language alternative
Median	Middle value, typical value
Mean	Average
IQR	Range of the middle 50% of values
Standard deviation	Typical distance from the average
Right-skewed	Pulled toward a few unusually high values
Symmetric	Roughly balanced above and below the center
Outlier	Unusually extreme value, far from the rest
Distribution	The pattern or spread of the values

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Statistical term	Plain-language alternative
Median	Middle value, typical value
Mean	Average
IQR	Range of the middle 50% of values
Standard deviation	Typical distance from the average
Right-skewed	Pulled toward a few unusually high values
Symmetric	Roughly balanced above and below the center
Outlier	Unusually extreme value, far from the rest
Distribution	The pattern or spread of the values

Statistical term

Plain-language alternative

Median

Middle value, typical value

Mean

Average

IQR

Range of the middle 50% of values

Standard deviation

Typical distance from the average

Right-skewed

Pulled toward a few unusually high values

Symmetric

Roughly balanced above and below the center

Outlier

Unusually extreme value, far from the rest

Distribution

The pattern or spread of the values

Writing a Complete Accessible Comparison

Let's walk through a fresh example from start to finish. A school administrator wants to know how two middle schools compare on a recent reading assessment. Here are the side-by-side box plots and summary statistics:

Side-by-side box plots of reading assessment scores on a warm cream background. Maple School has a muted teal box from about 68 to 79 with a median line at 74, navy whiskers from 55 to 94, and no outliers. Pine School has a muted orange box from about 58 to 75 with a median line at 66, navy whiskers from 42 to 98, and no outliers. Both share the same horizontal axis from 40 to 100 with crisp navy labels and the title Reading Assessment Scores.

Statistic	Maple School	Pine School
Shape	Roughly symmetric	Right-skewed
Mean	$74.2$ points	$69.5$ points
Median	$74.0$ points	$66.0$ points
SD	$8.3$ points	$12.1$ points
IQR	$11.0$ points	$17.0$ points
Min	$55$ points	$42$ points
Max	$94$ points	$98$ points

Since Pine School is right-skewed, we use median and IQR as our primary measures for both schools, following the guidance from Lesson 1 on pairing center and spread. Now let's write the comparison for the administrator — someone with no statistics training — using a simple four-part flow:

Set the scene. State what was measured and why it matters.
Compare typical values. Which school scored higher, and by how much?
Compare consistency. Which school's scores are more spread out?
Highlight anything unusual and recommend. Are there standout patterns? What does the evidence suggest?

Here is the result:

We compared reading scores at Maple School and Pine School on this year's assessment. A typical student at Maple School scored about $74$ points, while a typical student at Pine School scored about $66$ points — a gap of $8$ points. Scores at Pine School also varied more widely: the middle $50\%$ of students spanned $17$ points, compared to $11$ points at Maple School. Pine School did have a few very high scorers (the top score was $98$ ), but it also had students scoring as low as $42$ , suggesting a wider gap between the strongest and struggling readers. These results point to Pine School as the campus that would benefit most from targeted reading support.

Every element of our comparison checklist is covered, every claim includes a number, and every sentence uses language the administrator can follow without a statistics textbook.

Introduction

Why Your Audience Matters

Replacing Jargon with Plain Language

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Three Principles for Accessible Comparisons

Transforming a Technical Comparison

Writing a Complete Accessible Comparison

Staying Precise Without Jargon

Conclusion and Next Steps