Hi there, I'm Jayme Dyer.
When I was 17, I spent the summer volunteering at Yellowstone National Park.
An interesting thing happens in Yellowstone -
the wolves help the trees grow!
Which is not what you'd expect, right,
but that unlikely relationship was discovered with the help of some histograms.
A histogram displays the distribution of data in a sample, which can help scientists answer particular types of questions.
Wolves used to be common in and around Yellowstone, but by the 1920s,
people had killed off the last of them and an interesting thing happened to
the cottonwood trees after the last of the wolves were gone.
Typically a forest has a lot of young, small trees and a few older, large ones, but after the wolves
were gone the older larger trees remained while the smaller younger ones disappeared.
To try to figure out why, the scientists who published this cool paper -- they proposed two hypotheses:
Either a change in climate was making it hard for young cottonwoods to survive all over Yellowstone
or young cottonwoods were being eaten by too many elk.
See, one of the things that happened after the wolves were gone was that the number of elk increased dramatically.
Since elk liked to eat tree seedlings, more elk could mean less cottonwood trees, because they were being eaten.
To distinguish between these two hypotheses, scientists measured the diameter of cottonwood trees
in places where the elk were able to go
and in places where the elk were not able to go.
If the climate hypothesis were true, then small cottonwoods would be missing from all locations
because the climate change affects the entire park, but if the elk hypothesis were true, then
small cottonwoods would be missing only in places where elk were able to go.
Here are the results.
So, in places where the elk could go, the average tree diameter was bigger
and that's what you'd expect for the elk hypothesis
because if the elk are eating the small trees then there's fewer small trees in the sample,
so the only trees left to sample are bigger trees, so the average tree diameter should be bigger.
But the problem is, when you only look at averages, you can't tell what's actually going on with the small trees in the sample,
because you could get a bigger average in places where the elk could go
either: because there's fewer small trees
or because there's a few really big trees in those places.
That would bring up the average in both cases.
So you can't actually tell, just by looking at the average, what's going on with small trees.
You need to look at the distribution of tree sizes, and that's where a histogram comes in.
Here are the same data shown as histograms.
For each histogram, the scientists took the diameter measurements and divided them into size categories.
Then, for each size category they counted how many trees had a diameter in that category, and they plotted that number.
Then they did the same thing for all the size categories for all the trees.
The tallest bar tells you which category had the most number of trees of that size.
At the site where the elk could not go, there were a lot of trees with small diameters.
But at the site where the elk could go, there were many fewer - like none - of the smaller cottonwoods.
So, these data - and a whole lot of other data - combined to support the conclusion
that the young cottonwood trees were not growing in Yellowstone because they were being eaten by elk.
Interestingly, in 1996, wolves were reintroduced to Yellowstone, and pretty quickly, the elk population went down as the wolf population went up.
And as the elk population went down, the young cottonwood tree population went back up again.
That is how wolves helped cottonwood trees grow.
So, histograms are really useful,
because they show you information about the distribution of data
in a way that the average doesn't.
For example, these two hypothetical histograms represent two populations of imaginary trees that I made up.
They actually have the exact same average tree diameter and the same number of trees,
but one population has a lot more different sized trees - there's big trees and middle sized trees and small trees,
where the other population almost all of the trees are exactly the same size.
It's hard to tell that that's the distribution of trees just by looking at the averages, but when you look at the histogram,
it's really easy to tell really quickly that one population has a lot more diversity of size than the other population.
Alright, so let's switch gears for a second.
Check out this histogram of U.S. household income in 2018.
The height of the bar is the percent of families that made that much money.
It looks pretty good, right?
The highest bar is $50,000 to $75,000 a year.
That seems pretty good, but check out the size categories.
They're not uniform.
This size category has a spread of $25,000.
So, if you made $50,000 you got binned into that category and if you made $74,999 you got binned into that category
but in this size category this spreads only $5,000,
so, if you're $5,000 away from the lowest number, you get put into another bin.
So think about the effect that that has on the shape of the histogram. The data were published like this from the US Census Bureau,
but if I make some assumptions, I can make all the categories the same size.
That's a really different distribution, isn't it? It gives a really different impression of wealth in America, even though it's the same data.
So when you look at a histogram, check the size categories. Make sure they're all even, and
if they're not even, think about how that might change what the shape of the histogram is and
how that might change your interpretation of the data.
Histograms helped scientists understand the relationship between wolves and cottonwood trees in Yellowstone National Park
and histograms can be used to answer lots of really cool scientific questions,
if you know how to interpret them.