To create a relative frequency histogram, we first organize the data into classes and calculate the relative frequency for each class. Here's a step-by-step approach:

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Step 1: Organize the data into classes

The classes, as specified, start from 12 to 14, and we'll assume each class width is 2. The classes are:

1. 12–14
2. 15–17
3. 18–20

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Step 2: Tally the data

Count how many numbers from the dataset fall into each class:

• Dataset: $16, 19, 20, 12, 17, 18, 18, 16, 15, 18$
  1. 12–14: $12$ → 1 number
  2. 15–17: $16, 17, 16, 15$ → 4 numbers
  3. 18–20: $19, 20, 18, 18, 18$ → 5 numbers

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Step 3: Calculate relative frequency

The relative frequency for each class is the ratio of the count in that class to the total number of data points.

• Total number of data points = $10$
• Relative frequencies:
  1. 12–14: $\frac{1}{10} = 0.1$
  2. 15–17: $\frac{4}{10} = 0.4$
  3. 18–20: $\frac{5}{10} = 0.5$

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Step 4: Represent the data in a histogram

The histogram would show the classes on the x-axis and the relative frequencies on the y-axis. I'll create a visualization for this. matplotlib.pyplot as plt

Data for the histogram

classes = ["12-14", "15-17", "18-20"] relative_frequencies = [0.1, 0.4, 0.5]

Plotting the histogram

plt.bar(classes, relative_frequencies, color='blue', edgecolor='black')

Adding labels and title

plt.xlabel("Classes") plt.ylabel("Relative Frequency") plt.title("Relative Frequency Histogram")

Display the histogram

plt.show()Here is the relative frequency histogram. Each bar represents a class with its relative frequency:

• 12–14: Relative frequency = 0.1
• 15–17: Relative frequency = 0.4
• 18–20: Relative frequency = 0.5

Would you like me to break down the calculation or further explain how histograms work?

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Here are 5 questions to expand your understanding:

1. How would the histogram change if more students were recorded in the next 10 classes?
2. What is the difference between a relative frequency histogram and a frequency histogram?
3. How do you determine the class width for a dataset?
4. What are other types of graphs that can represent frequency data?
5. How would the histogram look if there were an additional class, like 21–23?

Tip: Always verify that the total of the relative frequencies adds up to 1 (or very close due to rounding).