Data in isolation is of limited value, but the more sets you have, the richer your profiling can become.
With a complete (DOB (DD MM YYY), Sex, Postcode ) tuple you can do a surprising amount of profiling against your relevant dataset.
EG: List of 10000 persons, . Average postcode contains 1000-2000 homes, potentially reducing your set by 50-75% immediately.
Sex (assuming M/F data capture) further reduces your remaining set by half.
If all you have is an estimated year of birth (ie: within 5 years), you can break that down into maybe 16 bands (assuming an even spread across a lifespan), each theoretically with 1.5% of the original population in them (156 persons)
With a wholly accurate year of birth, each of those bands holds 31 people.
If you have an accurate MM part of the birth date, your profiles now contain 13 & 2.6 respectively.
With an accurate DD part, you're now into reidentification territory.