Why add 1 to range?

Why add 1 to range?

• A. It accounts for rounding of scores during recording
• B. It corrects for decimal values
• C. It makes the range equal to the sample size
• D. It simplifies calculations

Answer: (A)

When scores are rounded to the nearest unit, the true endpoints can sit half a unit beyond the recorded minimum and maximum. So the actual spread could be a bit larger than just max minus min. Adding 1 to the range compensates for that potential half-unit on each end, giving an inclusive sense of the possible range. For example, if the recorded min is 20 and the max is 24, the observed range is 4, but accounting for rounding could push the true range up to 5 (from 19.5 to 24.5), which is captured by max − min + 1. The other reasons don’t fit this situation: adding 1 doesn’t fix decimals directly, doesn’t force the range to equal the sample size, and isn’t simply about simplifying calculations.

When scores are rounded to the nearest unit, the true endpoints can sit half a unit beyond the recorded minimum and maximum. So the actual spread could be a bit larger than just max minus min. Adding 1 to the range compensates for that potential half-unit on each end, giving an inclusive sense of the possible range. For example, if the recorded min is 20 and the max is 24, the observed range is 4, but accounting for rounding could push the true range up to 5 (from 19.5 to 24.5), which is captured by max − min + 1. The other reasons don’t fit this situation: adding 1 doesn’t fix decimals directly, doesn’t force the range to equal the sample size, and isn’t simply about simplifying calculations.