Junk Charts

The Periodic Table, a challenge in information organization

Reader Chris P. points me to this article about the design of the Periodic Table. I then learned that 2019 is the “International Year of the Periodic Table,” according to the United Nations.

Here is the canonical design of the Periodic Table that science students are familiar with.

(Source: Wikipedia.)

The Periodic Table is an exercise of information organization and display. It's about adding structure to over 100 elements, so as to enhance comprehension and lookup. The canonical tabular design has columns and rows. The columns (Groups) impose a primary classification; the rows (Periods) provide a secondary classification. The elements also follow an aggregate order, which is traced by reading from top left to bottom right. The row structure makes clear the "periodicity" of the elements: the "period" of recurrence is not constant, tending to increase with the heavier elements at the bottom.

As with most complex datasets, these elements defy simple organization, due to a curse of dimensionality. The general goal is to put the similar elements closer together. Similarity can be defined in an infinite number of ways, such as chemical, physical or statistical properties. The canonical design, usually attributed to Russian chemist Mendeleev, attained its status because the community accepted his organizing principles, that is, his definitions of similarity (subsequently modified).

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Of interest, there is a list of unsettled issues. According to Wikipedia, the most common arguments concern:

• Hydrogen: typically shown as a member of Group 1 (first column), some argue that it doesn’t belong there since it is a gas not a metal. It is sometimes placed in Group 17 (halogens), where it forms a nice “triad” with fluorine and chlorine. Other designers just float hydrogen up top.
• Helium: typically shown as a member of Group 18 (rightmost column), the  halogens noble gases, it may also be placed in Group 2.
• Mercury: usually found in Group 12, some argue that it is not a metal like cadmium and zinc.
• Group 3: other than the first two elements , there are various voices about how to place the other elements in Group 3. In particular, the pairs of lanthanum / actinium and lutetium / lawrencium are sometimes shown in the main table, sometimes shown in the ‘f-orbital’ sub-table usually placed below the main table.

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Over the years, there have been numerous attempts to re-design the Periodic table. Some of these are featured in the article that Chris sent me (link).

I checked how these alternative designs deal with those unsettled issues. The short answer is they don't settle the issues.

Wide Table (Janet)

The key change is to remove the separation between the main table and the f-orbital (pink) section shown below, as a "footnote". This change clarifies the periodicity of the elements, especially the elongating periods as one moves down the table. This form is also called "long step".

As a tradeoff, this table requires more space and has an awkward aspect ratio.

In this version of the wide table, the designer chooses to stack lutetium / lawrencium in Group 3 as part of the main table. Other versions place lanthanum / actinium in Group 3 as part of the main table. There are even versions that leave Group 3 with two elements.

Hydrogen, helium and mercury retain their conventional positions.

 

Spiral Design (Hyde)

There are many attempts at spiral designs. Here is one I found on this tumblr:

The spiral leverages the correspondence between periodic and circular. It is visually more pleasing than a tabular arrangement. But there is a tradeoff. Because of the increasing "diameter" from inner to outer rings, the inner elements are visually constrained compared to the outer ones.

In these spiral diagrams, the designer solves the aspect-ratio problem by creating local loops, sometimes called peninsulas. This is analogous to the footnote table solution, and visually distorts the longer periodicity of the heavier elements.

For Hyde's diagram, hydrogen is floated, helium is assigned to Group 2, and mercury stays in Group 12.

 

Racetrack

I also found this design on the same tumblr, but unattributed. It may have come from Life magazine.

It's a variant of the spiral. Instead of peninsulas, the designer squeezes the f-orbital section under Group 3, so this is analogous to the wide table solution.

The circular diagrams convey the sense of periodic return but the wide table displays the magnitudes more clearly.

This designer places hydrogen in group 18 forming a triad with fluorine and chlorine. Helium is in Group 17 and mercury in the usual Group 12 .

 

Cartogram (Sheehan)

This version is different.

The designer chooses a statistical property (abundance) as the primary organizing principle. The key insight is that the lighter elements in the top few rows are generally more abundant - thus more important in a sense. The cartogram reveals a key weakness of the spiral diagrams that draw the reader's attention to the outer (heavier) elements.

Because of the distorted shapes, the cartogram form obscures much of the other data. In terms of the unsettled issues, hydrogen and helium are placed in Groups 1 and 2. Mercury is in Group 12. Group 3 is squeezed inside the main table rather than shown below.

 

Network

The centerpiece of the article Chris sent me is a network graph.

This is a complete redesign, de-emphasizing the periodicity. It's a result of radically changing the definition of similarity between elements. One barrier when introducing entirely new displays is the tendency of readers to expect the familiar.

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I found the following articles useful when researching this post:

The Conversation

Royal Chemistry Society

 

Morphing small multiples to investigate Sri Lanka's religions

Earlier this month, the bombs in Sri Lanka led to some data graphics in the media, educating us on the religious tensions within the island nation. I like this effort by Reuters using small multiples to show which religions are represented in which districts of Sri Lanka (lifted from their twitter feed):

The key to reading this map is the top legend. From there, you'll notice that many of the color blocks, especially for Muslims and Catholics are well short of 50 percent. The absence of the darkest tints of green and blue conveys important information. Looking at the blue map by itself misleads - Catholics are in the minority in every district except one. In this setup, readers are expected to compare between maps, and between map and legend.

The overall distribution at the bottom of the chart is a nice piece of context.

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The above design isolates each religion in its own chart, and displays the spatial spheres of influence. I played around with using different ways of paneling the small multiples.

In the following graphic, the panels represent the level of dominance within each district. The first panel shows the districts in which the top religion is practiced by at least 70 percent of the population (if religions were evenly distributed across all districts, we expect 70 percent of each to be Buddhists.) The second panel shows the religions that account for 40 to 70 percent of the district's residents. By this definition, no district can appear on both the left and middle maps. This division is effective at showing districts with one dominant religion, and those that are "mixed".

In the middle panel, the displayed religion represents the top religion in a mixed district. The last panel shows the second religion in each mixed district, and these religions typically take up between 25 and 40 percent of the residents.

The chart shows that other than Buddhists, Hinduism is the only religion that dominates specific districts, concentrated at the northern end of the island. The districts along the east and west coasts and the "neck" are mixed with the top religion accounting for 40 to 70 percent of the residents. By assimilating the second and the third panels, the reader sees the top and the second religions in each of these mixed districts.

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This example shows why in the Trifecta Checkup, the Visual is a separate corner from the Question and the Data. Both maps utilize the same visual design, in terms of forms and colors and so on, but they deliver different expereinces to readers by answering different questions, and cutting the data differently.

 

P.S. [5/7/2019] Corrected spelling of Hindu.

An exercise in decluttering

My friend Xan found the following chart by Pew hard to understand. Why is the chart so taxing to look at? 

It's packing too much.

I first notice the shaded areas. Shading usually signifies "look here". On this chart, the shading is highlighting the least important part of the data. Since the top line shows applicants and the bottom line admitted students, the shaded gap displays the rejections.

The numbers printed on the chart are growth rates but they confusingly do not sync with the slopes of the lines because the vertical axis plots absolute numbers, not rates. 

The vertical axis presents the total number of applicants, and the total number of admitted students, in each "bucket" of colleges, grouped by their admission rate in 2017. On the right, I drew in two lines, both growth rates of 100%, from 500K to 1 million, and from 1 to 2 million. The slopes are not the same even though the rates of growth are.

Therefore, the growth rates printed on the chart must be read as extraneous data unrelated to other parts of the chart. Attempts to connect those rates to the slopes of the corresponding lines are frustrated.

Another lurking factor is the unequal sizes of the buckets of colleges. There are fewer than 10 colleges in the most selective bucket, and over 300 colleges in the largest bucket. We are unable to interpret properly the total number of applicants (or admissions). The quantity of applications in a bucket depends not just on the popularity of the colleges but also the number of colleges in each bucket.

The solution isn't to resize the buckets but to select a more appropriate metric: the number of applicants per enrolled student. The most selective colleges are attracting about 20 applicants per enrolled student while the least selective colleges (those that accept almost everyone) are getting 4 applicants per enrolled student, in 2017.

As the following chart shows, the number of applicants has doubled across the board in 15 years. This raises an intriguing question: why would a college that accepts pretty much all applicants need more applicants than enrolled students?

Depending on whether you are a school administrator or a student, a virtuous (or vicious) cycle has been realized. For the top four most selective groups of colleges, they have been able to progressively attract more applicants. Since class size did not expand appreciably, more applicants result in ever-lower admit rate. Lower admit rate reduces the chance of getting admitted, which causes prospective students to apply to even more colleges, which further suppresses admit rate. 

 

 

 

Book Preview: How Charts Lie, by Alberto Cairo

If you’re like me, your first exposure to data visualization was as a consumer. You may have run across a pie chart, or a bar chart, perhaps in a newspaper or a textbook. Thanks to the power of the visual language, you got the message quickly, and moved on. Few of us learned how to create charts from first principles. No one taught us about axes, tick marks, gridlines, or color coding in science or math class. There is a famous book in our field called The Grammar of Graphics, by Leland Wilkinson, but it’s not a For Dummies book. This void is now filled by Alberto Cairo’s soon-to-appear new book, titled How Charts Lie: Getting Smarter about Visual Information.

As a long-time fan of Cairo’s work, I was given a preview of the book, and I thoroughly enjoyed it and recommend it as an entry point to our vibrant discipline.

In the first few chapters of the book, Cairo describes how to read a chart. Some may feel that there is not much to it but if you’re here at Junk Charts, you probably agree with Cairo’s goal. Indeed, it is easy to mis-read a chart. It’s also easy to miss the subtle and brilliant design decisions when one doesn’t pay close attention. These early chapters cover all the fundamentals to become a wiser consumer of data graphics.

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How Charts Lie will open your eyes to how everyone uses visuals to push agendas. The book is an offshoot of a lecture tour Cairo took during the last year or so, which has drawn large crowds. He collected plenty of examples of politicians and others playing fast and loose with their visual designs. After reading this book, you can’t look at charts with a straight face!

***

In the second half of his book, Cairo moves beyond purely visual matters into analytical substance. In particular, I like the example on movie box office from Chapter 4, titled “How Charts Lie by Displaying Insufficient Data”. Visual analytics of box office receipts seems to be a perennial favorite of job-seekers in data-related fields.

The movie data is a great demonstration of why one needs to statistically adjust data. Cairo explains why Marvel’s Blank Panther is not the third highest-grossing film of all time in the U.S., as reported in the media. That is because gross receipts should be inflation-adjusted. A ticket worth $15 today cost $5 some time ago.

This discussion features a nice-looking graphic, which is a staircase chart showing how much time a #1 movie has stayed in the top position until it is replaced by the next higher grossing film.

Cairo’s discussion went further, exploring the number of theaters as a “lurking” variable. For example, Jaws opened in about 400 theaters while Star Wars: The Force Awakens debuted in 10 times as many. A chart showing per-screen inflation-adjusted gross receipts looks much differently from the original chart shown above.

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Another highlight is Cairo’s analysis of the “cone of uncertainty” chart frequently referenced in anticipation of impending hurricanes in Florida.

Cairo and his colleagues have found that “nearly everybody who sees this map reads it wrongly.” The casual reader interprets the “cone” as a sphere of influence, showing which parts of the country will suffer damage from the impending hurricane. In other words, every part of the shaded cone will be impacted to a larger or smaller extent.

That isn’t the designer’s intention! The cone embodies uncertainty, showing which parts of the country has what chance of being hit by the impending hurricane. In the aftermath, the hurricane would have traced one specific path, and that path would have run through the cone if the predictive models were accurate. Most of the shaded cone would have escaped damage.

Even experienced data analysts are likely to mis-read this chart: as Cairo explained, the cone has a “confidence level” of 68% not 95% which is more conventional. Areas outside the cone still has a chance of being hit.

This map clinches the case for why you need to learn how to read charts. And Alberto Cairo, who is a master visual designer himself, is a sure-handed guide for the start of this rewarding journey.

***

Here is Alberto introducing his book.

Pretty circular things

National Geographic features this graphic illustrating migration into the U.S. from the 1850s to the present.

 

What to Like

It's definitely eye-catching, and some readers will be enticed to spend time figuring out how to read this chart.

The inset reveals that the chart is made up of little colored strips that mix together. This produces a pleasing effect of gradual color gradation.

The white rings that separate decades are crucial. Without those rings, the chart becomes one long run-on sentence.

Once the reader invests time in learning how to read the chart, the reader will grasp the big picture. One learns, for example, that migrants from the most recent decades have come primarily from Latin America (orange) or Asia (pink). Migrants from Europe (green) and Canada (blue) came in waves but have been muted in the last few decades.

 

What's baffling

Initially, the chart is disorienting. It's not obvious whether the compass directions mean anything. We can immediately understand that the further out we go, the larger numbers of migrants. But what about which direction?

The key appears in the legend - which should be moved from bottom right to top left as it's so important. Apparently, continent/country of origin is coded in the directions.

This region-to-color coding seems to be rough-edged by design. The color mixing discussed above provides a nice artistic effect. Here, the reader finds out that mixing is primarily between two neighboring colors, thus two regions placed side by side on the chart. Thus, because Europe (green) and Asia (pink) are on opposite sides of the rings, those two colors do not mix.

Another notable feature of the chart is the lack of any data other than the decade labels. We won't learn how many migrants arrived in any decade, or the extent of migration as it impacts population size.

A couple of other comments on the circular design.

The circles expand in size for sure as time moves from inside out. Thus, this design only works well for "monotonic" data, that is to say, migration always increases as time passes.

The appearance of the chart is only mildly affected by the underlying data. Swapping the regions of origin changes the appearance of this design drastically.

 

 

 

 

 

Trump resistance chart: cleaning up order, importance, weight, paneling

Vox featured the following chart when discussing the rise of resistance to President Trump within the GOP.

The chart is composed of mirrored bar charts. On the left side, with thicker pink bars that draw more attention, the design depicts the share of a particular GOP demographic segment that said they'd likely vote for a Trump challenger, according to a Morning Consult poll.

This is the primary metric of interest, and the entire chart is ordered by descending values from African Americans who are most likely (67%) to turn to a challenger to those who strongly support Trump and are the least likely (17%) to turn to someone else.

The right side shows the importance of each demographic, measured by the share of GOP. The relationship between importance and likelihood to defect from Trump is by and large negative but that fact takes a bit of effort to extract from this mirrored bar chart arrangement.

The subgroups are not complete. For example, the only ethnicity featured is African Americans. Age groups are somewhat more complete with under 18 being the only missing category.

The design makes it easy to pick off the most disaffected demographic segments (and the least, from the bottom) but these are disparate segments, possibly overlapping.

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One challenge of this data is differentiating the two series of proportions. In this design, they use visual cues, like the height and width of the bars, colors, stacked vs not, data labels. Visual variety comes to the rescue.

Also note that the designer compensated for the lack of stacking on the left chart by printing data labels.

***

When reading this chart, I'm well aware that segments like urban residents, income more than $100K, at least college educated are overlapping, and it's hard to interpret the data the way it's been presented.

I wanted to place the different demographics into their natural groups, such as age, income, urbanicity, etc. Such a structure also surfaces demographic patterns, e.g. men are slightly more disaffected than women (not significant), people earning $100K+ are more unhappy than those earning $50K-.

Further, I'd like to make it easier to understand the importance factor - the share of GOP. Because the original form orders the demographics according to the left side, the proportions on the right side are jumbled.

Here is a draft of what I have in mind:

The widths of the line segments show the importance of each demographic segment. The longest line segments are toward the bottom of the chart (< 40% likely to vote for Trump challenger).

 

McKinsey thinks the data world needs more dataviz talent

Note about last week: While not blogging, I delivered four lectures on three topics over five days: one on the use of data analytics in marketing for a marketing class at Temple; two on the interplay of analytics and data visualization, at Yeshiva and a JMP Webinar; and one on how to live during the Data Revolution at NYU.

This week, I'm back at blogging.

McKinsey publishes a report confirming what most of us already know or experience - the explosion of data jobs that just isn't stopping.

On page 5, it says something that is of interest to readers of this blog: "As data grows more complex, distilling it and bringing it to life through visualization is becoming critical to help make the results of data analyses digestible for decision makers. We estimate that demand for visualization grew roughly 50 percent annually from 2010 to 2015." (my bolding)

The report contains a number of unfortunate graphics. Here's one:

I applied my self-sufficiency test by removing the bottom row of data from the chart. Here is what happened to the second circle, representing the fraction of value realized by the U.S. health care industry.

What does the visual say? This is one of the questions in the Trifecta Checkup. We see three categories of things that should add up to 100 percent. With a little more effort, we find the two colored categories are each 10% while the white area is 80%. 

But that's not what the data say, because there is only one thing being measured: how much of the potential has already been realized. The two colors is an attempt to visualize the uncertainty of the estimated proportion, which in this case is described as 10 to 20 percent underneath the chart.

If we have to describe what the two colored sections represent: the dark green section is the lower bound of the estimate while the medium green section is the range of uncertainty. The edge between the two sections is the actual estimated proportion (assuming the uncertainty bound is symmetric around the estimate)!

A first attempt to fix this might be to use line segments instead of colored arcs. 

The middle diagram emphasizes the mid-point estimate while the right diagram, the range of estimates. Observe how differently these two diagrams appear from the original one shown on the left.

This design only works if the reader perceives the chart as a "racetrack" chart. You have to see the invisible vertical line at the top, which is the starting line, and measure how far around the track has the symbol gone. I have previously discussed why I don't like racetracks (for example, here and here).

***

Here is a sketch of another design:

The center figure will have to be moved and changed to a different shape. This design conveys the sense of a goal (at 100%) and how far one is along the path. The uncertainty is represented by wave-like elements that make the exact location of the pointer arrow appear as wavering.

 

 

 

 

No Latin honors for graphic design

This chart appeared on a recent issue of Princeton Alumni Weekly.

If you read the sister blog, you'll be aware that at most universities in the United States, every student is above average! At Princeton,  47% of the graduating class earned "Latin" honors. The median student just missed graduating with honors so the honors graduate is just above average! The 47% number is actually lower than at some other peer schools - at one point, Harvard was giving 90% of its graduates Latin honors.

Side note: In researching this post, I also learned that in the Senior Survey for Harvard's Class of 2018, two-thirds of the respondents (response rate was about 50%) reported GPA to be 3.71 or above, and half reported 3.80 or above, which means their grade average is higher than A-.  Since Harvard does not give out A+, half of the graduates received As in almost every course they took, assuming no non-response bias.

***

Back to the chart. It's a simple chart but it's not getting a Latin honor.

Most readers of the magazine will not care about the decimal point. Just write 18.9% as 19%. Or even 20%.

The sequencing of the honor levels is backwards. Summa should be on top.

***

Warning: the remainder of this post is written for graphics die-hards. I go through a bunch of different charts, exploring some fine points.

People often complain that bar charts are boring. A trendy alternative when it comes to count or percentage data is the "pictogram."

Here are two versions of the pictogram. On the left, each percent point is shown as a dot. Then imagine each dot turned into a square, then remove all padding and lines, and you get the chart on the right, which is basically an area chart.

The area chart is actually worse than the original column chart. It's now much harder to judge the areas of irregularly-shaped pieces. You'd have to add data labels to assist the reader.

The 100 dots is appealing because the reader can count out the number of each type of honors. But I don't like visual designs that turn readers into bean-counters.

So I experimented with ways to simplify the counting. If counting is easier, then making comparisons is also easier.

Start with this observation: When asked to count a large number of objects, we group by 10s and 5s.

So, on the left chart below, I made connectors to form groups of 5 or 10 dots. I wonder if I should use different line widths to differentiate groups of five and groups of ten. But the human brain is very powerful: even when I use the same connector style, it's easy to see which is a 5 and which is a 10.

On the left chart, the organizing principles are to keep each connector to its own row, and within each category, to start with 10-group, then 5-group, then singletons. The anti-principle is to allow same-color dots to be separated. The reader should be able to figure out Summa = 10+3, Magna = 10+5+1, Cum Laude = 10+5+4.

The right chart is even more experimental. The anti-principle is to allow bending of the connectors. I also give up on using both 5- and 10-groups. By only using 5-groups, readers can rely on their instinct that anything connected (whether straight or bent) is a 5-group. This is powerful. It relieves the effort of counting while permitting the dots to be packed more tightly by respective color.

Further, I exploited symmetry to further reduce the counting effort. Symmetry is powerful as it removes duplicate effort. In the above chart, once the reader figured out how to read Magna, reading Cum Laude is simplified because the two categories share two straight connectors, and two bent connectors that are mirror images, so it's clear that Cum Laude is more than Magna by exactly three dots (percentage points).

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Of course, if the message you want to convey is that roughly half the graduates earn honors, and those honors are split almost even by thirds, then the column chart is sufficient. If you do want to use a pictogram, spend some time thinking about how you can reduce the effort of the counting!

 

 

 

 

 

Crazy rich Asians inspire some rich graphics

On the occasion of the hit movie Crazy Rich Asians, the New York Times did a very nice report on Asian immigration in the U.S.

The first two graphics will be of great interest to those who have attended my free dataviz seminar (coming to Lyon, France in October, by the way. Register here.), as it deals with a related issue.

The first chart shows an income gap widening between 1970 and 2016.

This uses a two-lines design in a small-multiples setting. The distance between the two lines is labeled the "income gap". The clear story here is that the income gap is widening over time across the board, but especially rapidly among Asians, and then followed by whites.

The second graphic is a bumps chart (slopegraph) that compares the endpoints of 1970 and 2016, but using an "income ratio" metric, that is to say, the ratio of the 90th-percentile income to the 10th-percentile income.

Asians are still a key story on this chart, as income inequality has ballooned from 6.1 to 10.7. That is where the similarity ends.

Notice how whites now appears at the bottom of the list while blacks shows up as the second "worse" in terms of income inequality. Even though the underlying data are the same, what can be seen in the Bumps chart is hidden in the two-lines design!

In short, the reason is that the scale of the two-lines design is such that the small numbers are squashed. The bottom 10 percent did see an increase in income over time but because those increases pale in comparison to the large incomes, they do not show up.

What else do not show up in the two-lines design? Notice that in 1970, the income ratio for blacks was 9.1, way above other racial groups.

Kudos to the NYT team to realize that the two-lines design provides an incomplete, potentially misleading picture.

***

The third chart in the series is a marvellous scatter plot (with one small snafu, which I'd get t0).

What are all the things one can learn from this chart?

• There is, as expected, a strong correlation between having college degrees and earning higher salaries.
• The Asian immigrant population is diverse, from the perspectives of both education attainment and median household income.
• The largest source countries are China, India and the Philippines, followed by Korea and Vietnam.
• The Indian immigrants are on average professionals with college degrees and high salaries, and form an outlier group among the subgroups.

Through careful design decisions, those points are clearly conveyed.

Here's the snafu. The designer forgot to say which year is being depicted. I suspect it is 2016.

Dating the data is very important here because of the following excerpt from the article:

Asian immigrants make up a less monolithic group than they once did. In 1970, Asian immigrants came mostly from East Asia, but South Asian immigrants are fueling the growth that makes Asian-Americans the fastest-expanding group in the country.

This means that a key driver of the rapid increase in income inequality among Asian-Americans is the shift in composition of the ethnicities. More and more South Asian (most of whom are Indians) arrivals push up the education attainment and household income of the average Asian-American. Not only are Indians becoming more numerous, but they are also richer.

An alternative design is to show two bubbles per ethnicity (one for 1970, one for 2016). To reduce clutter, the smaller ethnicites can be aggregated into Other or South Asian Other. This chart may help explain the driver behind the jump in income inequality.

 

 

 

 

 

Finding simple ways to explain complicated data and concepts, using some Pew data

A reader submitted the following chart from Pew Research for discussion.

The reader complained that this chart was difficult to comprehend. What are some of the reasons?

The use of color is superfluous. Each line is a "cohort" of people being tracked over time. Each cohort is given its own color or hue. But the color or hue does not signify much.

The dotted lines. This design element requires a footnote to explain. The reader learns that some of the numbers on the chart are projections because those numbers pertain to time well into the future. The chart was published in 2014, using historical data so any numbers dated 2014 or after (and even some data before 2014) will be projections. The data are in fact encoded in the dots, not the slopes. Look at the cohort that has one solid line segment and one dotted line segment - it's unclear which of those three data points are projections, and which are experienced.

The focus on within-cohort trends. The line segments indicate the desire of the designer to emphasize trends within each cohort. However, it's not clear what the underlying message is. It may be that more and more people are not getting married (i.e. fewer people are getting married). That trend affects each of the three age groups - and it's easier to paint that message by focusing on between-cohort trends.

***
Here is a chart that emphasizes the between-cohort trends.

A key decision is to not mix oil and water. The within-cohort analysis is presented in its own chart, next to the between-cohort analysis. It turns out that some of the gap between cohorts can be explained by people deferring marriage to later in life. The steep line on the right indicates that a bigger proportion of people now gets married between 35 and 44 than in previous cohorts.

I experimented a bit with the axes here. Several pie charts are used in lieu of axis labels. I also plotted a dual axis with the proportion of unmarried on the one side, and the corresponding proportion of married on the other side.