Statistics and Conversion of Units, a critical activity

Statistics and Conversion of Units, a critical activity

When working with data, the final result or the generated information can be presented as graphs, tables, statistics, hypothesis test results, indexes and other analysis appropriate to the type of data and the need. In general, the initial or collected data have a unit of measurement that is maintained in the data process and converted into information.

In this simple example, it is assumed that the table reflects the processed data and the units of measurement of the society or context of the people who process and will be users of what is obtained with this process. Changes, aggregation of data and information are made with the same units. The following table shows the Sales of a chemical product to the customers of a company, showing quantities sold, unit price (pounds and dollars) and sales revenue.

Imagine that now, someone needs the data in Table 1 in a place or context where the units of measurement are different (Soles and Kilograms). To use this data, it is enough with the conversions of the units of each of the concepts shown.

Basically there are two types of conversions, simple and compound. The conversion is a product sequence of fractions obtained from the equivalences. Equality (equivalence) is transformed into a fraction and the order, numerator and denominator are arranged so that the initial unit and the intermediate ones disappear; in the end only the desired units should remain.

Direct simple conversion

Example: Convert 120 Dollars to British Pounds

Equivalence: 1 dollar = 0.77 pounds, or 1 pound = 1.30 dollars

Calculation: 120 dollars * 1 pound / 1.30 dollars = 93.3. pounds

Simple compound conversion

Example: Convert 120 Dollars to Japanese Yen

Equivalence: 1 dollar = 0.77 pounds, or 1 pound = 1.30 dollars

1 pound = 141.80 yen, or: 1 yen = 0.0071 pounds

Calculation: 120 dollars * 1 pound / 1.30 dollars = 93.3. pounds

93.3 pounds * 141.80 yen / 1 pound = 13 229.94 yen

Actually, the process is unique:

120 dollars * 1 pound / 1.30 dollars * 141.8 yen / 1 pound = 13 229.94 yen

Composite conversion

Example: Convert 25 Km / Hour to miles / day

Equivalence: 1 mile = 1609 meters, 1 km = 1000 meters, 1 day = 24 hours (seems obvious, but it is necessary to have well-defined equivalences, self-sufficiency is a bad counselor)

Calculation: 25 km / hour * 1000 m / Km * 1 mile / 1609 meters * 24 hours / 1 day = 372.90 miles / day

Strictly speaking, the symbols of the units of measurement must be used, but for didactic reasons, we admit the possibility of writing the full name. If the data of origin, with the units of measurement that we want to convert, were already in Excel format, it would be enough to copy the table and into corresponding cells and place as a formula the operations necessary for the conversion. If in the cell corresponding to city Alpha and weight (in pounds) is the original value, 80 pounds, in the cell with the same position in the new table, the conversion sequence is written: 80 * 454/1 * 1 / 1000 The result will be 36.32 Kg.

Similar calculations are made for the cell cells of the weight and unit price. The income, as in the original table, is the product of the Quantity, now in Kg and the unit price, in soles. It can also be calculated by converting the income from the initial table (in dollars) directly to the value in the final table (in soles).

Taking as an example the data of the first row and column (Alpha City, Weight) with the value 80, the conversions will be

Quantity: 80 lb * 454 g / lb * 1kg / 1000 g = 36.32 Kg

Unit price: 800 US $ / lb * 2.2 lb / 1kg * 3.32 S /. / 1 US $ = 5.850, 2 Soles / Kg

Income: 36.32 Kg * 5850.2 S /. / Kg = 212,480 S /.

Or Good, Income: 64,000 US $ * 3.32 S /. / 1 US $ = 212,480 S /.

It is important to consider all units of equivalences to make the correct elimination and reach the new desired units.

The final picture will be:

For a good engineer the unit conversion process is elementary; for other people, a little practice or the help of someone who knows, plus the list of equivalents for the conversion and the use of the standard procedure, will allow them to change the data with one unit of measurement to others according to the need.