Private sector job growth and a recovering economy pushed Washington’s average wage in 2012 to $51,595. That’s the first time Washington’s average wage — for jobs covered by unemployment insurance — surpassed $50,000, the Employment Security Department said Wednesday. The 2012 increase was 3.4 percent from the year before. Much of the growth came from a 6.1 percent increase in the number of insured workers earning more than $75,000 in 2012. The average weekly wage rose from $959 to $992. Three state job sectors saw the highest gains in 2012: company management, up 17.6 percent; information, up 11.5 percent; and agriculture, up 11.5 percent. The state uses the average wage to calculate unemployment benefits. The minimum weekly unemployment benefit, calculated at 15 percent of the average weekly wage, will increase by $5 to $148, for new claims opened on or after July 7. At the same time, the maximum weekly benefit, calculated at 63 percent of the average weekly wage, will increase by $20, to $624. Currently, about 18 percent of unemployment-insurance claims are paid the maximum benefit amount, and 7 percent receive the minimum. The average is also used to compute company unemployment taxe and the state’s worker compensation benefit rate.