New section about data points

Adding a new section explain how to plot data points on top of the expected
cropped parabola.

README.md

@@ -202,3 +202,75 @@ cropped_parabola.png
 ```
 -->
 
+# Plotting Data Points
+A typical task in the advanced laboratory might be to compare measured data
+points to an expected function. Lets assume the expected function is the cropped
+parabola $`f(x)`$ from the previous examples. We will use random data points in
+this example, since we haven't actually measured real data, which is expected to
+follow $`f(x)`$.
+
+This example is based on the code from the previous example. Copy the file from
+the previous examples to `data_plot.py`, such that we an append to it and keep
+the function plotting code. Please add the code snippets in this section to the
+file `data_plot.py`.
+<!-- console
+```bash
+$ cp func_plot.py data_plot.py
+```
+-->
+
+We generate the pseudo data points by adding random deviations to the expected
+y-values. Lets assume we measured data points for all half-integer x-values.
+<!-- append data_plot.py -->
+```python
+x_data = np.array([-2.5, -2, -1.5, -1, -.5, 0, .5, 1, 1.5, 2, 2.5, 3])
+```
+
+We evaluate the function $`f(x)`$ again for the `x_data` values. The random
+deviations are drawn from a centered normal distribution with a standard
+deviation of 0.3. The third argument of `numpy.random.normal` specifies, how
+many random samples we want to draw. We use `len(x_data)`, since we want to draw
+a random deviation for each x-value.
+<!-- append data_plot.py -->
+```python
+y_data = x_data**2
+y_data[x_data >= 2] = 4
+y_data += np.random.normal(0, 0.3, len(y_data))
+```
+
+Finally we can add this to our plot. Since our data points are subject to
+statistical fluctuations, we would like to use matplotlib's `errorbar` method,
+which draw our data points with errorbars.
+
+<!-- append data_plot.py -->
+```python
+plt.errorbar(x_data, y_data, 0.3, fmt="ko", capsize=0)
+plt.savefig("measurement.eps")
+```
+
+The character `k` in the format parameter `fmt` sets the color to blac*k*, the
+`o` in `fmt` changes the style to *large dots*. The optional parameter `capsize`
+modifies the style of the error bars. You can play with these options and see
+what happens or have a look at the
+[documentation](https://matplotlib.org/api/_as_gen/matplotlib.axes.Axes.errorbar.html).
+
+<!-- append data_plot.py
+```python
+# We need also a png version of the plot to embed it into the README.md.
+plt.savefig("measurement.png")
+```
+-->
+
+<!-- console_output
+```
+$ python3 data_plot.py
+$ ls measurement.eps
+measurement.eps
+$ ls measurement.png
+measurement.png
+```
+-->
+
+After running `data_plot.py` you should have a plot similar to this.
+![Plot of cropped parabola with data points](https://srv.sauerburger.com/esel/FP-python-examples/-/jobs/artifacts/master/raw/measurement.png?job=doxec_test)
+