Dr. Valerie R. Bencivenga
Economics 329
PRACTICE HOMEWORK #1A:
ANSWERS
1.a.
discrete
b.
continuous
c.
discrete (dummy)
d.
discrete
e.
continuous (or approximately continuous)
2.a.
Mode
.
It does not make sense to average nuclear power plants and hydroelectric plants.
b.
Median
.
This variable probably has a skewed distribution, with a small number of households
having large net worth.
The mean would be distorted by this small number of large values of the
variable.
c.
Mean
.
There is no reason to think that this variable has a skewed distribution.
d.
Mean
.
There is no reason to think that this variable has a skewed distribution.
But if, upon
examining the data, it seems that a small number of workers work lots of overtime, and that this
will distort the mean, then the median would be preferred.
e.
Median
.
This variable probably has a very skewed distribution, where a small number of very
valuable homes would distort the mean.
3.a.
millions of hours per year, or just millions of hours.
b.
1/year or “per year” if the growth rate is stated as a proportional growth rate, and %/year or
“percent per year” if the growth rate is stated in percentage points (or just unit
free).
c.
(millions of hours per year)
2
, or (millions of hours)
2
.
d.
millions of hour per year times billions of dollars per year, or just millions of hours times billions
of dollars.
e.
unitfree.
4.a.
The mean will
increase,
because a positive value is being added to the original set of deviations.
b.
The variance will
increase.
The variance is
n
1
i
2
i
2
X
)
X
X
(
1
n
1
s
.
Obviously, if we add an
observation whose value equals
X
, the variance declines, because the sum of squared
deviations does not increase, and the denominator increases.
However, the addition of a value
above
X
will increase the mean
and
add a term to the sum
and
increase the denominator.
Intuitively, if we add an observation to the upper part of the distribution of the variable
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 Spring '12
 BENCIVENGA
 Economics, Standard Deviation, Variance, Mean

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