| Index | Carthage | New York | National |
| Average Test Scores | 52% | 56% | 48% |
| Student/Teacher ratio | n/a | n/a | 16:1 |
| Total public schools | 4 | 4,060 | 79,221 |
| Total private schools | 2 | 1,092 | 24,874 |
| Total post-secondary schools | n/a | 483 | 7,963 |
| Index | Carthage | New York | National |
| Completed 8th grade | 83.3% | 83.5% | 84.3% |
| Completed high school | 80.7% | 82.1% | 83.0% |
| Completed some college | 50.4% | 59.5% | 59.4% |
| Completed associate degree | 16.8% | 43.4% | 38.5% |
| Completed bachelors | 7.7% | 34.7% | 30.3% |
| Completed masters | 4.1% | 15.1% | 11.5% |
| Completed professional degree | 1.0% | 4.2% | 3.3% |
| Completed doctorate | 0.2% | 1.5% | 1.3% |
There are a total of 4 public schools, 2 private schools and n/a post-secondary schools in Carthage. Using the proficiency score averages, the average test scores for Carthage, NY schools is 52%. The average student to teacher ratio is n/a. In Carthage, NY, an average of 83.3% of students have completed 8th grade and an average of 80.7% have completed high school.
| City | Population | Avg. Test Scores | National Avg. |
| Lowville, NY | 3,329 | 68% | 41.7% |
| Calcium, NY | 3,548 | 67% | 39.6% |
| Philadelphia, NY | 1,196 | 63% | 30.2% |
| Antwerp, NY | 698 | 60% | 25.0% |
| Evans Mills, NY | 449 | 60% | 24.0% |
| Carthage, NY | 3,364 | 52% | 8.6% |
| City | Population | Avg. Test Scores | National Avg. |
| Heyburn, ID | 3,365 | 23% | 52.1% |
| Corunna, MI | 3,363 | 33% | 30.6% |
| Story City, IA | 3,362 | 86% | 78.6% |
| Palmyra, NY | 3,361 | 64% | 33.3% |
| Hoosick Falls, NY | 3,361 | 52% | 7.8% |
| Carthage, NY | 3,364 | 52% | 8.6% |
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