na-adjective, noun which may take the genitive case particle 'no', adverb, noun
unexpectedly; contrary to expectations; more than expected
Describes a result that is surprisingly different from what was anticipated, often with a nuance of 'more than expected' or 'contrary to what one thought'. Used as an adverb, adjectival noun, or noun.
存外、試験は簡単だった。
Unexpectedly, the exam was easy.
彼の料理は存外おいしかった。
His cooking was surprisingly delicious.
Compound of 存 (ぞん, 'think, suppose') and 外 (がい, 'outside'), literally 'outside of what one thought'. The exact historical derivation is uncertain, but the meaning follows naturally from the components.