This example describes a qualitative statistical study related to the eye colors of students in the Department of Mechanical Engineering. Let's break it down step by step:

Explanation

1. Variable Definition:

   • $X$: Represents the qualitative variable, which is the eye color of the students.
   • The possible values (modalities) of $X$, denoted as $M_i$ for $i = 1, 2, 3, 4$, are:
     • $M_1 = \text{Brown (Marron)}$
     • $M_2 = \text{Black (Noir)}$
     • $M_3 = \text{Blue (Bleu)}$
     • $M_4 = \text{Green (Vert)}$.

2. Sample Size:

   • The sample consists of 50 students ($n = 50$).

3. Frequency Table:

   • The qualitative series is summarized in a table, which shows:
     • The modalities $M_i$ (eye colors).
     • The effectifs $n_i$, i.e., the number of students with each eye color.
     • Total $\sum n_i = 50$.

   The table is structured as follows:

   Modalities ($M_i$)	Marron (Brown)	Noir (Black)	Bleu (Blue)	Vert (Green)	Total
   Effectifs ($n_i$)	20	19	5	6	50

Key Insights:

• The most frequent eye color is Brown (Marron) with 20 students.
• The least frequent eye color is Blue (Bleu) with only 5 students.
• Other frequencies are:
  • Black (Noir): 19 students.
  • Green (Vert): 6 students.

This table summarizes a qualitative distribution, commonly used in statistics to represent categorical data.

Would you like me to calculate proportions, percentages, or provide a graphical representation like a bar chart? Let me know!

Questions to Expand Understanding:

1. What are the proportions (relative frequencies) of each eye color in the sample?
2. How do we calculate the cumulative frequency for this distribution?
3. Can this data be represented graphically, and if so, which types of graphs would be appropriate?
4. What are the advantages of using a frequency table for qualitative data?
5. How could this data be used in further analysis or decision-making?

Tip:

When working with qualitative data, always ensure that the total frequencies add up to the sample size to avoid errors in your analysis.