## A Vehicle Fleet

A bus company has a fleet of 12 buses. Six of them were purchased seven years ago, three others were purchased three years ago, and the remaining three were purchased one year ago. All the buses enter the garage several times per year.

At the end of the year, the company owner checks the number of times that the buses were in the garage. He finds that the seven-year-old buses were in the garage 10 times each during the year, the three-year-old buses were in the garage eight times each during the year, and the new (one-year-old) buses were in the garage four times during the year. The question is how many times each bus entered the garage on the average.

We will organize the data:

• The target population – is the fleet of 12 buses. Each bus is an individual.

• The samples are the number of visits of a vehicle to the garage.

• The sample data are the specific number of garage visits by each individual bus.

The following illustration displays the sample data.

Illustration 3.3

In this example, each group has another characteristic In addition to the number of visits – the age of the buses in the group.

Sometimes it is more convenient to use the other characteristic for presenting the groups, as can be seen in the following table (column no. 2), which summarizes the data from the example.

Table 3.3

 Numbering of the Group Characteristics of the Group (age of the buses) Sample Data of the Group (garage visits) No. of Individuals in Each Group Weight of the Group Contribution of the Group to the Average 1 2 3 4 5 3=6 x 5 Group 1 7 years 10 visits 6 50% 5 visits Group 2 3 years 8 visits 3 25% 2 visits Group 3 1 year 4 visits 3 25% 1 visit Total 12 100% 8 visits

## Another Example – a Stock Exchange

Bill invests in shares of three companies listed on the stock exchange:

Caterpillar, McDonalds and Coca-Cola.

On the morning of January 1, 2008, the status of his investment was as follows (the figures are not real):

Table 3.4

 The Stock Exchange-listed Company No. of Shares Share Price Sum of the Investment 1 2 3 2=4 x 3 Caterpillar 12 \$6 \$72 McDonalds 6 \$10 \$60 Coca-Cola 2 \$30 \$60 Total 20 \$192

The investment totals \$192.

At the end of the trading day, the prices of all  shares held by Bill  rose sharply, as follows:

Table 3.5

 Name of Company Increase in % Increase in \$ (profit per share) Caterpillar 10% \$0.60 McDonalds 15% \$1.50 Coca-Cola 8% \$2.40

It is clear that Bill made a good profit on that day,and our first question is how many USDs on  average Bill earned (per share that he owned).

Organizing the data in the example:

The target population refers to the shares that Bill owns (20 shares).

The sample data are the profit in \$ on each share. We will organize the groups according to the sample data.

There are three different sample data:

\$0.60, \$1.50, and \$2.40.

Another characteristic of each group is that all the shares in each group relate to the same company, as follows:

All the shares that rose \$0.60 relate to Caterpillar.

All the shares that rose \$1.50 relate to McDonalds.

All the shares that rose \$2.40 relate to Coca-Cola.

Table3.6

 Numbering of the Group Characteristics of the Group (company names) Observation Data of the Group (profit per share in \$) Number of Individuals in Each Group Weight of the Group Contribution of Each Group to the Average 1 2 3 4 5 3=6 x 5 Group 1 Caterpillar \$0.60 12 60% \$0.36 Group 2 McDonalds \$1.50 6 30% \$0.45 Group 3 Coca-Cola \$2.40 2 10% \$0.24 Total 20 100% \$1.05 – average profit per share

The calculation shows (the bottom row of column no. 6) that the average profit per share was \$1.05. Bill’s profit totaled \$21 (= 20 shares X \$1.05 per share), constituting a 10.94% profit on the amount of the investment (\$192). We will present all the data in a table in the next slide.

## Calculating Profit Using Statistic Tools

Another obvious question relating to this example is how much profit (in terms of percentages) on average were earned by John on each USD of the 192 that he held on the stock exchange on January 1, 2008.

Before we perform this calculation, we will clarify our question.

If the result is 10%, for example, this would mean that John added 10% to the value of his original investment, i.e., \$19.20. In other words, \$0.10 (10%) was added for each USD invested.

We will format the data in a table:

John earned an average profit of 10.94% on his investment.

## Organizing the data

The target population is \$192. Every USD represents an individual in the target population.

The samples reflect the daily profit in percentages of each of the \$192 invested.

The sample data – there are only three different sample data sets: 10% (the Caterpillar shares), 15% (the McDonalds shares), and 8% (the Coca-Cola shares).

Arranging the groups – there are three groups corresponding to the three different sets of observation data.

We Will present all the data in a table.

Table 3.7

 No. of the Group Characteristics of the Group (company shares) Observation Data of the Group (profit in %) Number of Individuals in Each Group (Amount of Investment) Weight of the Group Contribution of the Group (Percentages) 1 2 3 4 5 3 = 6 X 5 Group 1 Caterpillar 10% \$72 37.50% 3.75% Group 2 McDonalds 15% \$60 31.25% 4.69% Group 3 Coca-Cola 8% \$60 31.25% 2.50% Total \$192 100% 10.94% average (2)

(1) The data are from columm no. 4 in Table 3.4

(2) The average profit as a percentage of the invesment