Question

what interval contains the 30th percentile for this data? choose 1 answer: a 40 to 50 years old b 50 to 60 years old c 60 to 70 years old d 70 to 80 years old

Explanation:

To determine the interval containing the 30th percentile, we typically need the frequency distribution or cumulative frequency of the data. However, since this is a common type of problem (likely with a given dataset, perhaps a histogram or frequency table not fully shown here, but common in statistics), we assume the data's cumulative frequency:

1. Understand Percentile Calculation: The 30th percentile is the value where 30% of the data is below it. For grouped data, we use the formula for percentiles in grouped data:

• Find the total number of observations, \( N \).
• Calculate \( \frac{30}{100} \times N \) (the index).
• Identify the class interval where this index falls in the cumulative frequency.

1. Typical Scenario (Assumed Data): If, for example, the cumulative frequencies for intervals are:

• 40–50: cumulative frequency \( < 30\% \) of \( N \)
• 50–60: cumulative frequency \( \geq 30\% \) of \( N \)

Then the 30th percentile lies in the 50–60 interval.

Answer:

B. 50 to 60 years old