When I am connected to internet via direct LAN wire the average google ping time is 64ms. But when I am connected to it via WLAN or wifi(through router) the average average google ping time goes up to 71ms. Is it normal to experience a delay of 6-7ms when connected via WLAN or my router taking longer.
Your router is one more "hop" along the way, so yes, this is normal. 5ms is not much, but realize that in this time your router receives the ICMP ping packet, determines where to route the packet, and forwards it.