What are the real limits for a score of X = 42, given measurements are recorded to the nearest half unit?

What are the real limits for a score of X = 42, given measurements are recorded to the nearest half unit?

• A. 41.75 and 42.25
• B. 41.5 and 42.0
• C. 41.75 and 42.0
• D. 41.5 and 42.25

Answer: (A)

Rounding to the nearest 0.5 sets clear cutoffs around the observed value. The true score that would still be recorded as 42 must lie between halfway marks to the neighboring recorded values. The midpoint between 41.5 and 42.0 is 41.75, and the midpoint between 42.0 and 42.5 is 42.25. So any true score from 41.75 up to 42.25 would be rounded to 42 (with the lower bound included and the upper bound effectively excluded). This gives the real-limit interval of 41.75 to 42.25, which is why the correct bounds are 41.75 and 42.25.

Rounding to the nearest 0.5 sets clear cutoffs around the observed value. The true score that would still be recorded as 42 must lie between halfway marks to the neighboring recorded values. The midpoint between 41.5 and 42.0 is 41.75, and the midpoint between 42.0 and 42.5 is 42.25. So any true score from 41.75 up to 42.25 would be rounded to 42 (with the lower bound included and the upper bound effectively excluded). This gives the real-limit interval of 41.75 to 42.25, which is why the correct bounds are 41.75 and 42.25.