add value in data group via REST API

It is the only way. Data-group records are not subcollections, so in order to replace one you have to replace them all. Here's some code I wrote for expanding and contracting data groups a while back in python:

def get_dg(rq, url, dg_details):
    dg = rq.get('%s/ltm/data-group/%s/%s' % (url, dg_details[0], dg_details[1])).json()
    return dg

def extend_dg(rq, url, dg_details, additional_records):
    dg = rq.get('%s/ltm/data-group/%s/%s' % (url, dg_details[0], dg_details[1])).json()

    current_records = dg['records']
    new_records = []
    for record in current_records:
        nr = [ {'name': record['name']}]
        new_records.extend(nr)
    for record in additional_records:
        nr = [ {'name': record}]
        new_records.extend(nr)

    payload = {}
    payload['records'] = new_records
    rq.put('%s/ltm/data-group/%s/%s' % (url, dg_details[0], dg_details[1]), json.dumps(payload))

def contract_dg(rq, url, dg_details, removal_records):
    dg = rq.get('%s/ltm/data-group/%s/%s' % (url, dg_details[0], dg_details[1])).json()

    new_records = []
    for record in removal_records:
        nr = [ {'name': record}]
        new_records.extend(nr)

    current_records = dg['records']
    new_records = [x for x in current_records if x not in new_records]

    payload = {}
    payload['records'] = new_records
    rq.put('%s/ltm/data-group/%s/%s' % (url, dg_details[0], dg_details[1]), json.dumps(payload))

if __name__ == "__main__":
    import requests, json

    b = requests.session()
    b.auth = ('admin', 'admin')
    b.verify = False
    b.headers.update({'Content-Type' : 'application/json'})

    b_url_base = 'https://172.16.44.5/mgmt/tm'

    dg_details = ['internal', 'myNetworks']
    net_changes = ['3.0.0.0/8', '4.0.0.0/8']

    print "\nExisting Records for %s Data-Group:\n\t%s" % (dg_details[1], get_dg(b, b_url_base, dg_details)['records'])
    extend_dg(b, b_url_base, dg_details, net_changes)
    print "\nUpdated Records for %s Data-Group:\n\t%s" % (dg_details[1], get_dg(b, b_url_base, dg_details)['records'])
    contract_dg(b, b_url_base, dg_details, net_changes)
    print "\nUpdated Records for %s Data-Group:\n\t%s" % (dg_details[1], get_dg(b, b_url_base, dg_details)['records'])