# General procedure

- `Set Scale` 100um -> 171 px
- `Set Measurements...` bounding rectangle, display label, Decimals 4, Redirect none
- `Measure` and `Clear Measurements` to produce a new and clear measuremens table
- Use the `Straight` tool to draw a line thta fits into the decarburated area
- Press `^+m` to add the measurement into the table
- Repeat the process at least 50 times

![Example of measurements.](measurements-example.jpg)

# Tasks

1. From microscope images get at least 50 measurements from each;
2. Export the `csv` file for each collection of measurements
3. Compute the basic descriptive statistics for each image:
   - sample size
   - mean
   - median
   - standard deviation
   - minimum
   - maximum
   - range
4. Compute the basic descriptive statistics for the complete dataset (200 measurements)
5. Prepare the following graphs:
   - One histogram for each image
   - Compare all histograms
   - One boxplot comparing the four zones (images)
6. Extract the following information:
   - central tendency,
   - spread,
   - possible outliers,
   - difference among images (zones)
7. State random variables
   - Define a random variable for the legth property
   - Define a discrete random variable, whose measurement is grater than a threshold (50um)
   - Define an indicator random variable that states:
     - $I_{ij} = 1$, if the measurement exceeds the threshold
     - $I_{ij} = 0$, otherwise
8. Compare images, based on your statistics and plots, answer the following:
   - Which image has the largest mean?
   - Which image has the greatest variability?
   - Do all images appear similar?
   - Does one image seem to come from a different population?
9. Your `Readme.md` file must include:
   - Introduction
   - Random variables background
   - Objective
   - Description of the data
   - Table of the descriptive statistics
   - Required plots and its description
   - Definition of random variables
   - Comparison of images
   - Conclusions
   - Attach the 4 `csv` files
10. Your report must answer the following
    - What is the measured variable in your experiment?
    - Why can this variable be modeled as a random variable?
    - Which of your proposed variables are continuous?
    - Which of your proposed variables are discrete?
    - Which image has the highest mean value?
    - Which image has the largest dispersion?
    - What does your threshold analysis indicate?
    - What can you conclude about the variability of the measurements.
