Final answer:
Guilford warned against using divisors smaller than 20 for calculating percentages because of potential inaccuracies with small sample sizes. Other examples provided include the impossibility of determining how many students out of 200 receive a certain amount of aid without additional data, and correct rounding practices when reporting numerical answers.
Step-by-step explanation:
Joy Paul Guilford (1965) cautioned that it is unwise to compute percentages with divisors smaller than 20. Guilford's point was that smaller sample sizes can lead to misleading or unstable percentage calculations because the variance can be quite large; larger samples tend to provide more reliable and stable percentage estimates.
If we now turn to a practical example, consider a scenario where if a sample of 200 students is taken to determine how many are expected to receive $250 or more in financial assistance, the answer cannot be determined with the information provided. This is because we would require additional data about the proportions or likelihood of this financial threshold being met.
When performing calculations, such as determining a price with tax added using a calculator, if the result is 201.867, it's essential to report the answer rounded to the hundredths place as 201.87 because the digit dropped (7) prompts rounding up.
Regarding percentages, if in a given community, 49.7 percent is under the age of 35, this gives a clear demographic profile. Similarly, in statistical distributions, statements such as 'at least 25 percent of the values are equal to one' help to understand the distribution of data.