To solve this problem, I'll guide you through each of the tasks you've asked for, assuming you're working with grouped data. Please share the data distribution or a sample table showing the frequency for each class interval. Here's an outline of what we'll cover based on common grouped data problems:

1. Histogram and Frequency Polygon

• A histogram visually represents the frequency of each class interval with bars.
• A frequency polygon connects the midpoints of each class interval with a line graph.

I can help construct these once I have the data.

2. Balanced or Lopsided

• This typically refers to the skewness of the distribution:
  • Balanced (Symmetrical): If the frequencies are equally distributed around a central point.
  • Lopsided (Skewed): If most of the data is concentrated on one side. If it's skewed right, the tail is on the right. If it's skewed left, the tail is on the left.

3. Relative Frequency for 600-624

Relative frequency is calculated as: $\text{Relative Frequency} = \frac{\text{Frequency for the class}}{\text{Total Frequency}}$ You'd need to provide the class frequency for the range 600-624.

4. Cumulative Frequency for 525-549

Cumulative frequency is the sum of frequencies up to and including the current class interval. Once you provide the class intervals and frequencies, I can calculate this.

5. Percentile Rank for the Range 550-574

The percentile rank $P(x)$ for a class interval is calculated using the formula: $P(x) = \frac{L + \frac{f(x)}{2}}{\text{Total Frequency}} \times 100$ Where:

• $L$ is the sum of the frequencies below the class.
• $f(x)$ is the frequency of the class interval in question.

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Please share the data distribution table to proceed with the calculations!

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Example Follow-up Questions:

1. What is the class interval structure in your data?
2. What are the total frequencies for each class?
3. Would you like help with calculating skewness for this data?
4. Should we explore how to interpret skewness (lopsided) visually?
5. Do you need help plotting the graphs digitally?

Tip: In a frequency distribution, the cumulative frequency can help you understand what percentage of data falls below a certain threshold!