(working-with-histograms)=
#  Walkthrough: Working with Histograms 
**(25 minutes)**

Let\'s create a simple histogram:

    [] TH1D h1("hist1","Histogram from a Gaussian",100,-3,3)

:::::{note}
Let's think about what these arguments mean for a moment (and also look
at the description of `TH1D` on the ROOT web site). 

   - The ROOT name of the histogram is `hist1`.

   - The title displayed when plotting the
histogram is "Histogram from a Gaussian".[^f26] 

   - There are 100 bins in the histogram.

   - The limits of the histogram are from -3 to 3.

:::{admonition} Question
:class: tip
What is the width of one bin of this histogram? Type the
following to see if your answer is the same as ROOT thinks it is:

    [] h1.GetBinWidth(0)

Note that we have to indicate which bin's width we want (bin 0 in this
case), because you can define histograms with varying bin
widths.[^f27]
:::
:::::

If you type

    [] h1.Draw()

right now, you won't see much. That's because the histogram is empty.
Let's randomly generate 10,000 values according to a distribution and
fill the histogram with them:

    [] h1.FillRandom("gaus",10000)
    [] h1.Draw()

The "gaus" function is pre-defined by ROOT (see the `TFormula` class
on the ROOT web site; there's also more {ref}`later in this tutorial
<fitting-histogram>`). The default Gaussian distribution has a width
of 1 and a mean of zero.

You've probably already noticed the words "Mean" and "StdDev" in the
upper right-hand corner of the plot. If you need formal definitions,
you can find them in Equations {eq}`eqn:mean` and {eq}`eqn:stddev`
later in this tutorial.

:::{admonition} Question 
:class: tip
For those who know statistics: In this histogram, why
isn't the mean exactly 0, nor the width exactly 1?
:::

Add another 10,000 events to histogram `h1` with the `FillRandom`
method (use up-arrow to enter the command again). Click on the canvas.
Does the histogram update immediately, or do you have to type another
`Draw` command?

Let's put some error bars on the histogram. Select {menuselection}`View --> Editor`,
then click on the histogram. From the {guilabel}`Error` pop-up menu, select
{guilabel}`Simple`. Try clicking on the {guilabel}`Simple Drawing` box and see how the
plot changes.

:::::{note}
With these options, the size of the error bars is equal to the square
root of the number of events in that histogram bin. Use the up-arrow key
in the ROOT command window and execute the `FillRandom` method a few
more times; draw the canvas again. 

:::{admonition} Question
:class: tip
Why do the error bars get
smaller? Hint: Look at how the y-axis changes.
:::

You will often want to draw histograms with error bars. For future
reference, you could have used the following command instead of the
Editor:

    [] h1.Draw("e")
:::::

Let's create a function of our own:

    [] TF1 myfunc("myfunc","gaus",0,3)

The "gaus" (or Gaussian) function is actually
$P_{0}e^{- \frac{1}{2}\left( \frac{\left( x - P_{1} \right)}{P_{2}} \right)^{2}}$,
where $P_{0}$, $P_{1}$, and $P_{2}$ are "parameters" of the function. Let's
set these three parameters to values that we choose, draw the result,
and then create a new histogram from our function:

    [] myfunc.SetParameters(10.,1.0,0.5)
    [] myfunc.Draw()
    [] TH1D h2("hist2","Histogram from my function",100,-3,3)
    [] h2.FillRandom("myfunc",10000)
    [] h2.Draw()

Note that we could also set the function\'s parameters individually:

    [] myfunc.SetParameter(1,-1.0)
    [] h2.FillRandom("myfunc",10000)

:::{admonition} Question
:class: note
What's the difference between `SetParameters` and `SetParameter`?
If you have any doubts, check the description of class `TF1` on the
ROOT web site.
:::

:::{figure-md} sports-fig
:class: align-center

<img src="https://imgs.xkcd.com/comics/sports.png" alt="xkcd sports" width="45%">

<https://xkcd.com/904/> by Randall Munroe
:::

[^f26]: Did you just ask "What is a 'Gaussian'?" I created a 
    section on {ref}`statistics <statistics>`
    just for you! 

[^f27]: *For advanced users:* Why would you have varying bin widths?
    Recall the "too many bins" and "too few bins" examples that I showed
    in the introduction to the class. In physics, it's common to see
    event distributions with long "tails." There are times when it's a
    good idea to have small-width bins in regions with large numbers of
    events, and large bin widths in regions with only a few events. This
    can result in having a large number of events in every bin in the
    histogram, which helps with fitting to functions as discussed below
    and in {ref}`the statistics section <statistics>`.