The frequency distribution shown represents the number of farms per state for the 50 United States, based on information from the U.S. Department of Agriculture. Determine the average number of farms per state from these data. The mean computed from the original ungrouped data was 41,796 and the standard deviation was 38,856. How do your answers for these grouped data compare? Why might they differ?

Number of Farms per State f

0–under 20,000 ...............16

20,000–under 40,000 ............11

40,000–under 60,000 ............11

60,000–under 80,000 ............ 6

80,000–under 100,000 .......... 4

100,000–under 120,000 ........... 2