# Statistics

## Data Presentation and Analysis - The Stock Exchange:

### 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:

 All of the shares that rose by\$1.50 are Caterpillar shares. All of the shares that rose by \$0.60 are Citigroup shares. All of the shares that rose by \$2.40 are Coca-Cola shares.

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?