Quantitative Data Organization and Distribution Analysis

Histograms serve as the primary and most essential graphical organization technique for quantitative data analysis.
Initial visual inspection of raw data yields significant structural insight during preliminary exploratory analysis:
- The lowest value in the dataset is observed at $49$ .
- The highest frequency or concentration of data values occurs in the upper seventies ( $70\text{s}$ ).

Defining Data Classes:
- Determine and define the appropriate class intervals (bins) based explicitly on the specifics and range of the quantitative dataset.
Selecting Graphical Methods:
- Select optimal graphical representation methods designed to display the dataset effectively.
Histogram Construction and Distribution Modeling:
- Construct the histogram by plotting the frequency of data across the defined classes.
- Draw a continuous curve directly on top of the visual bars of the digital histogram to expose the underlying probability distribution.

Characterizing the Distribution Curve:
- Analyze the shape of the superimposed curve to determine the continuous distribution of the dataset.
Symmetry Assessment:
- Check whether the distribution exhibits symmetry relative to a baseline reference point (such as zero).
Classifying Asymmetric Distributions:
- If a distribution is non-symmetric, identify its directional skewness:
- Right Scale (Right-Skewed / Positively Skewed): The elongated tail of the distribution extends toward higher values on the right side.
- Left Scale (Left-Skewed / Negatively Skewed): The elongated tail of the distribution extends toward lower values on the left side.