John invests in shares of three companies listed on the stock exchange:
Citigroup, Caterpillar and Coca-Cola.
On the morning of January 1, 2008, the status of his investment was as follows (note: the figures are not not actual results):
|
The Stock Exchange-listed Company |
No. of Shares |
Share Price |
Sum of the Investment |
|
(1) |
(2) |
(3) |
(4) = (2) X (3) |
|
Citigroup |
12 |
$6 |
$72 |
|
Caterpillar |
6 |
$10 |
$60 |
|
Coca-Cola |
2 |
$30 |
$60 |
|
Total |
20 |
|
$192 |
The investment totals $192.
At the end of the trading day, the price of all shares that John held rose sharply, as follows:
|
Name of Company |
Increase in % |
Increase in $ (profit per share) |
|
Citigroup |
10% |
$0.60 |
|
Caterpillar |
15% |
$1.50 |
|
Coca-Cola |
8% |
$2.40 |
It is clear that John earned a good profit on that day, and our first question is how many USDs on average did John earn per share that he owned?
There are three different pieces of data: $0.60, $1.50, and $2.40.
Another characteristic of each group is that all shares in each group have been issued by the same company, as follows:
|
|
|
We will present all of the data in a table:
|
Numbering of the Group |
Names of the Companies |
Profit per share in $ (the value) |
Number of Individuals in Each Group (the frequency) |
Weight of the Group (the relative frequency) |
Contribution of the Group to the Average |
|
(1) |
(2) |
(3) |
(4) |
(5) |
(6) = (3) x (5) |
|
Group 1 |
Citigroup |
$0.60 |
12 |
60% |
$0.36 |
|
Group 2 |
Caterpillar |
$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.
Calculating the Average Profit on Each USD Invested
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:
|
Numbering of the Group |
Names of the Companies |
Profit in % (the value) |
Number of Items in Each Group (the frequency) |
Weight of the Group (the relative frequency) |
Contribution of the Group (Percentages) |
|
(1) |
(2) |
(3) |
(4) (1) |
(5) |
(6) = (3) x (5) |
|
Group 1 |
Citigroup |
10% |
$72 |
37.50% |
3.75% |
|
Group 2 |
Caterpillar |
15% |
$60 |
31.25% |
4.69% |
|
Group 3 |
Coca-Cola |
8% |
$60 |
31.25% |
2.50% |
|
Total |
|
|
$192 |
100% |
10.94% average (2) |
John earned an average profit of 10.94% on his investment.
Activity
Try to locate the average income and the median income of families in the USA on the US Census Bureau website. Which of these is larger?
If your answer is the average income, then you were correct!
The distribution of incomes in the USand most other countries indicates that relatively few families have very high incomes, while many families have low incomes. Thus, the high-income families have a greater effect on the average income than in the median income.
In order to enable a better understanding of this subject, we will use an extreme example. We will assume that there are 20 people in a restaurant, each of whom earns an income of $30,000 annually. Clearly, both the median income and the average income will be $30,000 per year. Let us now assume that another person comes into the restaurant. This individual is very rich, with an income which is 100 times the income of those sitting in the restaurant. In this case, the median income will not change, but the average income will increase from $30,000 to approximately $170,000.
