cohort mean. The distributions of cohorts 7-9 were slightly right-skewed. The
distributions of cohorts 2-6 were approximately symmetric. Kurtosis coefficients were
all positive and of similar magnitude for cohorts 1-9. They imply that each cohort had a
higher probability of extreme sizes than would occur if the distribution of farm size
within the cohort were normal.
The moments for the tenth cohort were very different from the others. It is readily
apparent that this cohort contained some very large farms. The estimated median and
mean values were very different. The standard deviation was much larger than for any of
the other cohorts. The large skewness coefficient implies a highly right-skewed
distribution. The very large kurtosis coefficient further documents that much of the
variance was due to infrequent extreme deviations as opposed to frequent modest-sized
deviations.
In subsequent censuses, size ranges of the cohorts overlapped since farms within a
designated 1992 cohort could expand or contract operational size over time. The four
moments, median, and range width for each incumbent cohort are reported for 1997 and
2002 in Table 2. The most dramatic and prevalent results for each of the first nine
cohorts were: (1) the gap between median and mean farms increased over time, (2) the
values of the higher moments became much larger, and (3) the size range of the cohort
widened greatly, in most cases 50-100 times wider. For cohort 10, the gap between
median and mean farms and the size of its standard deviation also increased over time,
but its skewness and kurtosis coefficients were actually smaller in 1997 and 2002 than in
1992. Consequently, for each of the first nine cohorts in both 1997 and 2002 censuses,
size distributions became considerably flatter and more asymmetric with a thicker left
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