The following class limits would be acceptable for developing a frequency distribution on income:

$0 - $5,000

$5,001 - $10,000

$10,001 - $20,000

Over $20,000

Question

The following class limits would be acceptable for developing a frequency distribution on income:

$0 - $5,000

$5,001 - $10,000

$10,001 - $20,000

Over $20,000

BlackTom AI · Accepted Answer

When evaluating class limits for a frequency distribution, the key requirement is that the intervals are consecutive, non-overlapping, and cover the range of data without leaving gaps.
Option 1: True. Saying the given class limits are acceptable would imply that they form a perfect, gap-free sequence for continuous data. However, with income as a continuous variable, the gap between 5000 and 5001 creates a nonempty interval (5000 < income < 5001) that is not represented by any class. This makes the intervals effectively incomplete for a continuous distribution, so this option is not correct.
Option 2: False. This option correctly challenges the idea that the specified limits are acceptable. The proposed classes are 0–5000, 5001–10000, 10001–20000, and over 20000. For continuous data, to avoid gaps, Class 1 would need to end at 5000.999... and Class 2 would begin at 5000.999... (or, more practically, the next whole-number boundary that aligns with the data, such as 5000–9999 or 5000–10000 depending on convention). With discrete dollars, some instructors accept 0–5000, 5001–10000, etc., but this still leaves an implicit gap between 5000 and 5001, which is problematic for a true continuous-frequency distribution. Therefore, the statement as written is not acceptable, making this option correct.
Option 3: (Not applicable here since the question presents only two choices, but if considered, any assertion that there must be a single universally “correct” way to lay out intervals would be overly strict; in practice, the acceptability depends on whether the intervals are defined to be inclusive/exclusive and whether they cover all possible values without gaps.)
Option 4: (Also not applicable for the same reason as above; the core issue is the gap that can exist between 5000 and 5001 for continuous data, which invalidates the proposed limits as acceptable in a standard frequency distribution.)

The following class limits would be acceptable for developing a frequency distribution on income: $0 - $5,000 $5,001 - $10,000 $10,001 - $20,000 Over $20,000判断题

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