For Angular 1.3+ (credits to @Tom)

Use an alias expression (Docs: Angular 1.3.0: ngRepeat, scroll down to the Arguments section):

<div ng-repeat="person in data | filter:query as filtered">
</div>

For Angular prior to 1.3

Assign the results to a new variable (e.g. filtered) and access it:

<div ng-repeat="person in filtered = (data | filter: query)">
</div>

Display the number of results:

Showing {{filtered.length}} Persons

Fiddle a similar example. Credits go to Pawel Kozlowski