ECO 230
Marianna Kudlyak
Economic Statistics
Spring 2007
Answer Key to Homework #2
Total points: 10. Graded exercises: Ex.1 (2 points), Ex.4 (2 points), Ex. 6 (2 points), and Ex.
7 (2 points). 0.5 points were added for the presence of each of the remaining 4 exercises.
Exercise 1. A survey of 12 students at a local university asked approximately how many
hours per week they spend on the Internet. Their answers are listed below.
1
3
0
5
8
2
2730
1
51
2
1
3
1
6
a)
What are the mean and median for this data?
Using the formula for sample mean: mean is 9.5
To obtain a median, order the data in ascending order:
0
0
3
5
7
8
12
13
13
15
16
22
Median is 8+(1/2)*(128) = 8+2=10
b)
From the data presented above, calculate the first and third quartiles.
1
st
quartile: (1/4)*(n+1)th observation = 3.25th observation = 3+(1/4)*(53) = 3+2/4=3.5
3
rd
quartile: (3/4)*(n+1)th observation = 9.75th observation = 13+(3/4)*(1513) =
13+(6/4) = 14.5
c)
From the data presented above calculate the interquartile range.
3
rd
quartile  1
st
quartile = 14.53.5 = 11
d)
What is the coefficient of variation for this data?
Using the value of the standard deviation from part e) below,
CV =
=
x
s
6.82/9.5 = 0.72 or 72%
e)
What is the variance and the standard deviation for this data?
Using the formulas for sample standard deviation and sample variance:
s
2
=
=
−
−
∑
=
1
12
)
(
12
1
2
i
i
x
x
46.45
s = 6.82
f)
What is the range of this data?
Range is Max – Min = 220=22
Exercise 2. Inflation rates in small country for the past five years have been 10%, 7%, 13%,
9%, and 12%.
a)
What is the average annual rate of inflation?
Use the geometric mean to calculate the mean inflation rates:
{(10)(7)(13)(9)(12)]
1/5
= 9.96536
b)
If this rate of inflation continues, how long will it take for prices to double?
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View Full DocumentNumber of years for the inflation to double at this growth rate:
Solve the
following equation for x:
(1.0996536)
X
= 2.0.
Take the log of both sides of the equation:
X log(1.0996536) = log (2.0).
Simplify:
X = .301029996/.0412559 = 7.297 years
Exercise 3. Newbold, Carlson and Thorne, Problem 3.31 p.64.
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 Spring '08
 Kudlyak
 Standard Deviation, Sample standard deviation, Newbold, Thorne

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