APFIVE Rounding Error In Relative Frequencies
After computing the relative frequencies in a survey, a researcher rounded each percentage separately. This rounding caused the summed percentages to exceed 100%. What mistake did the researcher make during the rounding process?
Rounded Percentage Table from Survey Data
| School Length (days) | Frequency | Rounded Percent |
|---|---|---|
| 180 | 1100 | 56% |
| 160 | 300 | 16% |
| 200 | 500 | 26% |
| No opinion | 100 | 7% |
A
He divided each frequency by an incorrect total number of respondents before rounding.
B
He mistakenly replaced the ratios with their reciprocals during the rounding process.
C
He converted decimals to percentages by multiplying by 100 twice, resulting in inflated values.
D
He rounded each category’s percentage independently, leading to cumulative rounding errors that caused the total to exceed 100%.
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