WARNING: THE EDGAR SYSTEM ENCOUNTERED ERROR(S) WHILE PROCESSING THIS SCHEDULE.
<TABLE> <S> <C>
<ARTICLE> 6
<RESTATED>
<CIK> 0000882899
<NAME> NUVEEN TAX-FREE UNIT TRUST
<SERIES> Series 678
<NAME> MICHIGAN INSURED TRUST
<NUMBER> 48
<MULTIPLIER> 1
<CURRENCY> U.S. DOLLARS
<FISCAL-YEAR-END> FEB-29-2000
<PERIOD-START> MAR-01-1999
<PERIOD-END> FEB-29-2000
<PERIOD-TYPE> YEAR
<EXCHANGE-RATE> 1
<INVESTMENTS-AT-COST> 3,639,948
<INVESTMENTS-AT-VALUE> 3,588,625
<RECEIVABLES> 69,274
<ASSETS-OTHER> 0
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 3,657,899
<PAYABLE-FOR-SECURITIES> 0
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 13,881
<TOTAL-LIABILITIES> 13,881
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 0
<SHARES-COMMON-STOCK> 38,022
<SHARES-COMMON-PRIOR> 38,650
<ACCUMULATED-NII-CURRENT> 57,260
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> 1,000
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> -51,323
<NET-ASSETS> 3,644,018
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 210,553
<OTHER-INCOME> 0
<EXPENSES-NET> 5,740
<NET-INVESTMENT-INCOME> 204,813
<REALIZED-GAINS-CURRENT> 1,348
<APPREC-INCREASE-CURRENT> -241,637
<NET-CHANGE-FROM-OPS> -35,476
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> 205,987
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 40,000
<NUMBER-OF-SHARES-REDEEMED> 1,978
<SHARES-REINVESTED> 0
<NET-CHANGE-IN-ASSETS> -301,243
<ACCUMULATED-NII-PRIOR> 58,434
<ACCUMULATED-GAINS-PRIOR> -347
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> 0
<GROSS-ADVISORY-FEES> 0
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> 0
<AVERAGE-NET-ASSETS> 0
<PER-SHARE-NAV-BEGIN> 0
<PER-SHARE-NII> 0
<PER-SHARE-GAIN-APPREC> 0
<PER-SHARE-DIVIDEND> 0
<PER-SHARE-DISTRIBUTIONS> 0
<RETURNS-OF-CAPITAL> 0
<PER-SHARE-NAV-END> 0
<EXPENSE-RATIO> 0
[AVG-DEBT-OUTSTANDING] 0
[AVG-DEBT-PER-SHARE] 0
</TABLE>