Exercises on Statistics I
3. Composite ratios
COMPOSITE RATIOS
Exercise 1
A farmer cultivates corn on two lands. The following is known about the cultivation:
Location of
Distribution of Distribution of cultivated
cultivated
harvest in 2000 (%)
land in 2008 (%)
land
Fairytopia
60
30
Narnia
40
70
Total
Corn per acre (ton)
2000
2008
7.5
10.0
12.5
13.2
Questions:
a) Determine the average yield of corn for both years.
b) How many percentages did the productivity grow with on average per year?
Exercise 2
A shipping company takes on orders in three categories. The following is known about the fares:
Truck weight
Lighter than 5 tons
Between 5 and 12 tons
Heavier than 12
Total
Run kms in
2003 (%)
Total income in
Average fare
2007 (%)
in 2007(HUF/km) in 2003 (HUF/km)
99
90
162
150
309
300
…
…
In 2003 half of the kms were run by the lightest trucks while the heaviest ones run only one fifth of
the total.
In 2007, 40% of the total income was generated by the trucks heavier than 12 tons, while the
incomes from the other two categories equaled.
Questions:
a.) Fill in the missing data in the table.
b.) Determine the average fare price for both years.
c.) With how many percentages did the average fare price grow per year?
Exercise 3
An underwear sewing company has noticed that there is a significant difference between the quality
of male and female underwear sewing. The following data are known about production:
Shifts
I.
II.
III.
Total
Distribution of underwear
production (%)
Male
Female
Rate of not up to standard
underwear (%)
Male
Female
5.5
6.5
4.5
8.5
4.0
4.0
Exercises on Statistics I
3. Composite ratios
They also know that 30% of the male underwear production came from the second shift while the
1st and the third shifts shared production equally. 20% of female underwear was sewed in the first
shift while the third shift’s proportion equaled that of the male underwear.
Questions:
a) Fill in the gaps of the statistical table.
b) Determine the average fare price for both types of underwear.
c) Which factors influence the difference between the average rates of defectives?
Exercise 4
A product of a manufacturing firm is produced in both of the plants of the firm, one in Budapest and
the other in the countryside. The following data are known about the production.
Plant
Distribution of
Production in
production costs in
2007 (%)
2008 (%)
Budapest
Countryside
Total
Unit costs
Change by 2008
In 2007
compared to 2007
(HUF/piece)
(HUF)
2500
+400
2000
+400
…
…
In 2007 the plants shared production equally, while in 2008, production costs were 20% higher in
Budapest.
Questions:
a.) Fill in the missing data in the table.
b.) Determine the average fare price for both years.
Exercise 5
A college library examined the library visiting habits of college students. The following was
published:
Year
First
Second
Third
Total
Distribution of
students in 2003
(%)
…
30
25
…
Number of
borrowed books
(books) in 2008
1 500
2 400
…
5 100
Number of borrowed books per student
in 2003
in 2008
Change
(book/head)
(book/head) (2003 = 100 %)
5
…
-40
8
6
…
…
…
-20
…
4.25
…
Questions:
a.) Fill in all the missing data in the table.
b.) Determine the average number of borrowed books in 2003. How many books did third year
students borrow on average in 2007?
c.) With how many percentages did the average number of borrowed books drop per year?