Andrew E. Jones
Math 214-002
Lab 2: Barley Harvests
Purpose: The purpose of this lab report is to compare several aspects of barley crops from 1972
to 1995 on a state by state basis as well as the entire US as a whole. By examining the
differences from state to state and over the course of time we hope to notice any trends that may
occur that would affect the production of barley.
Introduction: The Department of Agriculture collects various statistics concerning crops and crop
harvests each year. We will be looking at some statistics that were collected from 1972 to 1995
regarding the barley harvests for each year. Among the statistics we will be examining are ratios
between amounts planted and harvested (in thousands of acres) and the number of bushels
produced (in thousands).
First we will be looking at the numbers concerning North Dakota’s (ND) barley harvest and
production as it is by far the country’s most proficient producer of the crop. In 1987 the US saw
a record amount of barley crops being produced, with ND alone producing over 25% of the total
harvest. Though the amounts planted, harvested and produced vary and don’t always agree in
regards to which state is the most proficient at growing, ND is consistently at the top of each
category each year.
To get started we will look at the raw statistics concerning ND’s harvests from 1972 to 1995.
Descriptive Statistics: ND Harvest (in Thousands of Acres)
Variable
ND Harvest
N
24
N*
0
Mean
2446.5
SE Mean
95.6
StDev
468.2
Minimum
1500.0
Q1
2110.0
Median
2450.0
Q3
2740.0
Maximum
3450.0
North Dakota’s mean harvest is a staggering 2,446,500 acres on average each year, which is
almost 28% of the average total US harvest. This number is quite close to the median harvest of
2,450,000. This indicates a fairly consistent harvest coming from North Dakota, an assumption
that is confirmed by the relatively small standard deviation of 468,200 acres (relatively small
when concerning agriculture, that is). The median and standard deviation leads one to predict the
grouping of harvests by amount should be fairly centralized, so let’s look at a histogram
depicting the actual amounts.
Histogram of ND Harvest
7
6
Frequency
5
4
3
2
1
0
1500
2000
2500
3000
ND Harvest (in Thousands of Acres)
3500
Andrew E. Jones
The histogram of North Dakota’s harvest in thousands of acres matches our expectations.
Namely, the number for the harvests are centered around 2,5000,000 acres, but that the graph has
more of a peak than a sloping curve. The bars at either end of the histogram that portray
extremes of harvests are quite small. This is exactly what you want to see if you are a farmer; it
means that harsh periods of time for crop production don’t last extremely long and that barley
prices will remain fairly stable. The slight increase around 2,000,000 acres is indicative of
slower/harsher years resulting in this lower harvest, an idea that will be confirmed when looking
at a plot of ND’s harvests over time.
Time Series Plot of ND Harvest
ND Harvest (in Thousands of Acres)
3500
3000
2500
2000
1500
1972
1976
1980
1984
Year
1988
1992
Andrew E. Jones
When looking at the amount of barley harvested in North Dakota over the years you immediately
noticed a drastic decline from 1978 to 1980. These corresponds exactly with a heat wave and
drought that hit in 1980, one that was so severe it was published by the National Oceanic and
Atmospheric Administration as one of the US’s billion-dollar weather disasters. The few years
that followed this incident the state saw record highs for harvests, a number that I find perplexing
as I wasn’t able to find information as to why. I suspect the government stepped in to assist
farmers by improving infrastructure followed by a period that would have resulted in good yields
without intervention, but this is mere speculation. After these record highs and lows the amount
of barley harvested by North Dakota appears to stabilize, so let’s look at their actual production
statistics.
Descriptive Statistics: ND Production (in Thousands of Bushels)
Variable
ND Production
N
24
N*
0
Mean
111107
SE Mean
7691
StDev
37678
Minimum
45150
Q1
85503
Median
104015
Q3
137003
Maximum
184250
Their average production of barley was approximately 111,107,000 bushels per year. Their
median production of 104,015,000 bushels appears to be significantly different than the mean, an
observation that is confirmed by a standard deviation of 37,678,000 which is proportionally
larger than those seen in their harvests. On face value these numbers indicate that the histogram’s
bars representing ND’s production will be less centralized than that seen for harvests. Let’s see if
this hypothesis stands true.
Histogram of ND Production
7
6
Frequency
5
4
3
2
1
0
40000
60000
80000 100000 120000 140000 160000
ND Production (in Thousands of Bushels)
180000
Andrew E. Jones
As was guessed the bars for the production of barley in North Dakota are not as centralized as
those seen for the harvest. The actual production of barley in bushels is still centered about the
median and mean (specifically around 100,000,000 bushels), though the extremes seem to be in
disagreement with the statistics concerning harvests. While this is quite interesting to see it is
also quite easy to explain. In seasons of drought a farmer might still be able to harvest the land of
his planted barley, but the actual production of it would drop as some of what he harvested
would be unable to be sold as it would be dead. The same conclusion can be drawn of the other
extreme. In years where a farmer harvests the same about of land he may get a better yield, and
thus production, if the growing season is quite good. Let’s take a look at the amount of barley
produced by North Dakota over the years.
Time Series Plot of ND Production
ND Production (in Thousands of Bushels)
200000
175000
150000
125000
100000
75000
50000
1972
1976
1980
1984
Year
1988
1992
Andrew E. Jones
The production drop in 1980 coincides with the low numbers seen for harvest. However, the
slight declines that were seen in the harvest’s time plot around 1974 and 1988 are much more
pronounced for production. These drops, not surprisingly, also coincide with other billion-dollar
droughts caused by heat waves. Looking at the plot as a whole reveals that actual production of
barley is much more sporadic than that of harvests. This fact reveals a disparity between the
amount harvested and the amount produced. Specifically, even though more land is harvested
more barley is not necessarily produced as a lot of it may be unusable.
Now that we’ve looked at the trends concerning the harvests and production of barley for a
single state we should look at the statistics for the country as a whole.
Descriptive Statistics: US Harvest (in Thousands of Acres)
Variable
US Harvest
N
24
N*
0
Mean
8753
SE Mean
317
StDev
1555
Minimum
6279
Q1
7528
Median
8528
Q3
9726
Maximum
11974
The mean harvest for the entire Unites States is 8,753,000 acres. This number is astonishing
considering North Dakota alone accounts for 2,446,500 acres. The median amount of barley
harvested is 8,528,000 acres, which is close to that of the average. What jumps out at me,
though, is a standard deviation of 1,555,000 acres. Such a large deviation implies that the amount
of barley harvested in each state varies wildly. This seems to mesh with the sheer amount of
barley produced in North Dakota in relation to the country as a whole. For confirmation we can
look to a histogram representation of these numbers.
Histogram of US Harvest
4
Frequency
3
2
1
0
6000
7200
8400
9600
10800
US Harvest (in Thousands of Acres)
12000
Andrew E. Jones
The histogram peaks at two bars, representing a harvest of 7,8000,000 and 8,400,000 acres. The
distribution shows that the amount of barley harvested each year is almost normalized.
Presumably this is due to just a few Midwestern states being harvesting the majority of all
barley. When those states have a bad harvest due to harsh weather it affects the entire United
States, causing the bars of the histogram to be so close in height. Another observation is the
distinct lack of a bar centered at 10,8000,000 acres. At first I dismissed this observation thinking
that it only indicates that within the 24 years of statistics the combined total harvest within the
Unites States did not fall within 10,200,000 and 11,4000,000 acres. However, this fact in of itself
is fascinating. It represents a period of time where the number of acres harvest for barley
skyrocketed by over 1,000,000, then suddenly plummeted down to a more normalized level. My
prediction is that this coincides with the level of high harvest and production seen in 1984 to
1986, but I delay my justification until this is confirmed by looking at the time plot.
Time Series Plot of US Harvest
US Harvest (in Thousands of Acres)
12000
11000
10000
9000
8000
7000
6000
1972
1976
1980
1984
Year
1988
1992
Andrew E. Jones
The amount of barley harvested by the entire United States does indeed peak between the years
that I had predicted. My reason for predicting this surge of harvested barley is due to the drought
that occurred in 1980. The heat wave that prevented a large harvest of barley during those couple
years would have caused the prices for it to go up dramatically in the couple of years that
followed. This fact would incentivize farmers to drastically increase the amount of barley they
produce in order to sell what barley they could at such high prices. This would also account for
the reduction in harvest in the years that follow as the prices would have dropped dramatically
with a large influx of barley and subsequent price drop. Next we will look at the statistics
concerning the US’s actual production of barley.
Descriptive Statistics: US Production (in Thousands of Bushels)
Variable
US Production
N
24
N*
Mean
0 437956
SE Mean
17499
StDev
85729
Minimum
289994
Q1
380123
Median
421958
Q3
499580
Maximum
608532
The average production of barley for the entire United States is 437,956,000 bushels, 25% of
which is from North Dakota which follows the trend we have already noticed. The median for
production was 421,958,000 bushels, a number fairly close to the mean. The standard deviation
of 85,729,000 bushels seems to be quite large, so I’m interested in what the histogram
representing these numbers will look like.
Histogram of US Production
9
8
7
Frequency
6
5
4
3
2
1
0
300000
350000
400000
450000
500000
550000
US Production (in Thousands of Bushels)
600000
Andrew E. Jones
The frequency distribution for the production of the Unites States as a whole is particularly
interesting. Ignoring the bar centered around 600,000,000, the observation would be that the
histogram and by extension production of barley appear to be fairly normal. However, since we
cannot simply disregard the outliers in this case those occurrences cause the entire histogram to
be shifted. Given the previous trends for production and harvests it is safe to assume that these
happened between 1984 and 1986, which will be confirmed when we glance at the time plot.
Time Series Plot of US Production
US Production (in Thousands of Bushels)
650000
600000
550000
500000
450000
400000
350000
300000
1972
1976
1980
1984
Year
1988
1992
Andrew E. Jones
As expected the three years of record breaking barley production are 1984, 1985 and 1986. The
years of low production that were previously seen in North Dakota’s time plots are also in the
graph for the entirety of the United States which confirms our knowledge of there being a
drought during those periods (although my cursory research on the subject had already
acknowledged that). What is interesting to note is the apparent lack of stability in barley
production over the course of time. The schema of production seems to always be headed
towards a high or low point and rarely at a stable level. This pattern is also present when looking
at just North Dakota’s production of barley.
Since we’ve looked at both the production and harvest of barley, let’s now look at the relation
between barley that is planted and that which is harvested.
Scatterplot of Harvested vs Planted for California
Harvested (in Thousands of Acres)
1100
1000
900
800
700
600
500
400
300
200
200
400
600
800
1000
Planted (in Thousands of Acres)
1200
Andrew E. Jones
Picking a state at random, in this case California, reveals a linear relationship between the
amount for barley that is planted and harvested. While this state was chosen for no particular
reason, the linear nature holds true for every state. When more barley is planted, more is harvest.
This makes sense as a farmer would want to harvest what they’ve planted in order to make as
much profit as possible. One would expect, then, that if more barley was planted that more
would be produced, but we know this is not the case. That expectation isn’t realized as droughts
or other natural factors can kill crops. So even though those crops would be harvested a larger
percentage of them would be unusable, hence hurting actual production.
Conclusion: There are several things to note about this report that apply not only to barley, but of
all crops. Heat waves cause drought and, no matter how much preparation is made, can obliterate
crop yields. These periods tend to cause an increase in price for the crop, which is then over
produced in the following seasons in an effort to maximize profits due to the price hikes. These
droughts have long lasting effects on not just production of the crop but also the economics that
surround them. These trends are most recognizable when looking at a time plot; they give the
viewer a sense of how a couple bad years can lead to over production as soon as the drought is
over. These trends aren’t recognizable when one looks at these statistics via a histogram. They
only allow the observer to see where the median of production lie without a sense of time. Both
of these graphs, along with the statistics that back them, are important tools for agriculturalists
and economists alike.