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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.

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That's not normal. Average wireless latencies are in the microseconds. My bet is that you just happened to hit a different Google data center. Test against a site that doesn't have data centers around the world. – David Schwartz Sep 13 '12 at 17:56
@DavidSchwartz I even did ping to modem ip, with simple LAN it was less than 0ms but via router it was 3ms. – Ali Arslan Sep 13 '12 at 18:03
Weird. It sounds like you have an unusually slow router, at least in responding to pings. – David Schwartz Sep 13 '12 at 18:46
Do a traceroute instead of a ping. A traceroute shows the latency per-hop and is almost always a more useful troubleshooting tool. If you are really seeing 7ms latencies to your local router, then I would replace that piece of junk with something better, my linux-based routers tend to only add ~1-2ms on low-end equipment. – Zoredache Sep 13 '12 at 23:02

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.

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