To determine the class containing the 80th percentile from the histogram, we can follow these steps:

1. Calculate the Total Frequency:

Add up the frequencies of all the classes.

From the histogram:

• 10-20: 8
• 20-30: 12.5
• 30-40: 7.5
• 40-50: 3
• 50-60: 2
• 60-70: 1
• 70-80: 1

$\text{Total Frequency} = 8 + 12.5 + 7.5 + 3 + 2 + 1 + 1 = 35$

2. Determine the 80th Percentile Position:

Calculate the position in the data set corresponding to the 80th percentile.

$\text{80th Percentile Position} = 0.8 \times 35 = 28$

3. Identify the Class Containing the 28th Data Point:

• First class (10-20): Cumulative frequency = 8
• Second class (20-30): Cumulative frequency = 8 + 12.5 = 20.5
• Third class (30-40): Cumulative frequency = 20.5 + 7.5 = 28

The 28th data point falls within the cumulative frequency of the third class (30-40).

Answer:

The class containing the 80th percentile is (C) 30-40.

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Would you like more details or have any questions? Here are some related questions:

1. What is the 50th percentile (median) class from the histogram?
2. How do you interpret the percentile rank in a distribution?
3. How do you determine the interquartile range (IQR) from a histogram?
4. What are some common mistakes when interpreting percentiles in histograms?
5. How can you use cumulative frequency to find other percentiles?

Tip: When calculating percentiles from a histogram, always ensure you correctly sum the frequencies and calculate the cumulative frequencies accurately.