Here’s the solution to the questions based on the provided image:

2.1 Identification and Classification of the Variable

The variable being studied is age. It is a quantitative discrete variable because it is measured in integers (ages) and represents countable data.

2.2 Frequency Table

I’ll create a table of absolute frequencies (the count of occurrences for each age), relative frequencies (proportion), and cumulative frequencies:

2.3 Bar Chart

I'll create a bar chart to represent the absolute frequencies visually. Let me generate that for you..pyplot as plt

Data for the bar chart

ages = [14, 15, 16, 17, 18] absolute_frequencies = [2, 6, 6, 4, 2]

Creating the bar chart

plt.figure(figsize=(8, 6)) plt.bar(ages, absolute_frequencies, width=0.6, edgecolor='black') plt.title("Bar Chart of Ages", fontsize=14) plt.xlabel("Ages", fontsize=12) plt.ylabel("Absolute Frequency", fontsize=12) plt.xticks(ages) plt.grid(axis='y', linestyle='--', alpha=0.7) plt.showHere is the bar chart representing the absolute frequencies of the ages.

2.4 Amplitude of the Circular Sector for Age 17

To determine the amplitude of the sector in a pie chart for students aged 17:

1. The relative frequency of age 17 is $20\%$.
2. The total circle is $360^\circ$, so: $\text{Amplitude} = \frac{\text{Relative Frequency (\%)}}{100} \times 360$ $\text{Amplitude} = \frac{20}{100} \times 360 = 72^\circ$

Thus, the amplitude of the circular sector for students aged 17 is 72°.

Would you like further clarification or another type of visualization?

Related Questions:

1. How can you interpret cumulative frequency data in this context?
2. What is the significance of relative frequencies in a classroom setting?
3. How can the distribution of ages impact group activities in class?
4. How could a histogram differ from a bar chart in this scenario?
5. How would the calculation change if there were a larger class size?

Tip:

Always cross-check the cumulative frequency with the total count to ensure data consistency