WASHINGTON — The preliminary national average price received by farmers for all wheat in January was $6.86 per bu, down 33c from $7.19 in December but up 17c from $6.69 in January 2011, the U.S. Department of Agriculture said in its latest Agricultural Prices report.

The average price paid for winter wheat in January was $6.25 per bu, down 16c from $6.41 a bu in December and down 10c from $6.35 in January 2011. The average price paid for durum was $8.87 a bu, down $1.13 from $10 in December but up $1.78 from $7.09 a year earlier. Spring wheat other than durum averaged $7.86 a bu, down 40c from $8.26 in December but up 72c from $7.14 in January 2011.

The average price paid for rough rice in January was $14.50 a cwt, up 30c from $14.20 in December and up 50c from $14 a year earlier.

The January index of prices received by farmers for food grains was 225 compared with the 1990-92 base of 100, down 4% from 235 the previous month but up 2% from 220 in January 2011.

The January index of feed grains was 255, up 1% from 253 in December and up 22% from 209 in January 2011. The average price paid to farmers for corn was $5.90 a bu, up 4c from $5.86 in December and up 96c from $4.94 in January 2011. Farmers received an average of $10.40 a cwt for grain sorghum in January, down 10c from $10.50 in December but up 91c from $9.49 in January 2011. The average price paid for oats in January was $3.62 a bu, up 5c from $3.57 in December and up 49c from $3.13 in January 2011.

The index of January prices received for oilseeds was 211, down about 1% from 212 in December but up 2% from 207 in January 2011. Farmers received an average of $11.70 a bu for soybeans in January, up 20c from $11.50 in December and up 10c from $11.60 in January 2011.

The January index for dairy products was 147, down 3% from 152 in December but up 15% from 128 in January 2011. The average price for all milk in January was $19 a cwt, up 40c from $18.60 in December and up $2.40 from $16.60 in January 2011.

The January poultry and egg index was 152, down 6% from 162 in December but up 8% from 141 in January 2011. The average price paid to farmers for all eggs in January was 77c a dozen, down 20c from 97c in December but up 1c from 76c in January 2011.