Of course this is going to sound like a shameless plug, but honestly, the easiest way to do this is with the Prelert Anomaly Detective app.
Using the QuickMode feature, you can literally put this search in:
index=whatever NOT(date_wday=saturday) NOT(date_wday=sunday) | timechart count by tms_logcat limit=0
and Anomaly Detective will automatically take care of baselining the normal occurrence rate of each error type ("tms_logcat") and will offer you the ability to alert on this data on-going with a one-click ability to schedule the search to run in the background every 5 minutes for example. How it works video: http://support.prelert.com/customer/portal/articles/1417340-quickmode
By the way, don't get caught up in trying to use standard deviation as your approach to express anomalousness. Standard deviation assumes that the data samples (in this case, "counts of errors") conforms to a nice, symmetrical Gaussian Bell curve. In most cases, counts of things are better modeled by Poisson curves. Anomaly Detective automatically figures out the best statistical model for your data to maximize accuracy and minimize false alerting.